I immediately thought of several things that bother me during play, both as a player and a GM, but I tend to avoid confronting the other player about them. Doing so can potentially lead to a bigger disruption of the game than the bad behavior. However, not doing anything to curb those annoying habits might mean that your (and the other players') dissatisfaction and resentment continues to fester unchecked, which isn't healthy, either.
I've decided to present a handful of my personal pet peeves here, and--more importantly--try to give some advice for how to avoid being guilty of them yourself. I encounter these issues far more often in organized play than in home games. The latter gives more control over who you play with, so it's usually easier to avoid the players who set you off. But even in a group you've been with for some time, and are very comfortable with, you'll want to stay alert for these behaviors.
The player who doesn't know what their character's go-to attack and skill modifiers are, or where to find them on the character sheet, even after playing the character for quite some time.
Your GM has many characters to keep track of, while you just have the one (and maybe a companion). Therefore, you, not your GM, should be responsible for being the expert on what your PC can do. At the very least, you need to know what your modifiers are for the activities your character will engage in most often--whether that's your signature attack, your best noncombat skill, or just what your Perception and Initiative modifiers are.
Naturally, players who are new to the system, or to RPGs in general, should be cut some slack here. But once you've played a character for a while, you should be ready and able to answer the GM's most common questions about their stats. And yes, those numbers will constantly change as you advance in level and acquire better gear, but you still need to be able to find them quickly on your character sheet in order to keep the game moving along at a reasonable pace.
The player who has to be reminded of a basic rule that directly impacts their character's options, every single fight, week after week.
This peeve is very closely related to the last one, but involves more general knowledge and mastery of the rules. If your GM has to keep reminding you week after week that you can only attack once after moving more than 5 ft., or that you can't combine a standard action (like Vital Strike) with a charge, or that trying to shoot someone adjacent to you provokes attacks of opportunity, it will get old fast. Invest just a little more time in learning the rules, and everyone at the table will have more fun.
Ideally, everyone should possess their own copy of the rulebook and have a working knowledge of how to find a rule they need, even if they haven't read the entire text. (I don't hold other people to my own practice of reading RPG rulebooks from cover to cover...as much as I might sometimes wish they would.) Review the rules that affect your character most often until you start to internalize them. For example, Pathfinder's action economy of standard, move, swift, immediate, and full-round actions can be one of the more confusing parts of the game, but it's also one of the basic rules elements that everyone needs to learn in order to attain any degree of mastery of that system.
Ideally, everyone should possess their own copy of the rulebook and have a working knowledge of how to find a rule they need, even if they haven't read the entire text. (I don't hold other people to my own practice of reading RPG rulebooks from cover to cover...as much as I might sometimes wish they would.) Review the rules that affect your character most often until you start to internalize them. For example, Pathfinder's action economy of standard, move, swift, immediate, and full-round actions can be one of the more confusing parts of the game, but it's also one of the basic rules elements that everyone needs to learn in order to attain any degree of mastery of that system.
The player who built their character around a single killer combo, but then can't explain clearly how it works, or how they calculated the bonuses they're claiming.
It comes with the territory of a crunchy system like Pathfinder that part of the appeal is optimizing a character to do one or two things really, really well. Exploiting the rules to the fullest requires a broad knowledge of all the resources available for the game, which requires a significant investment of time and money to acquire those books, to study them, and to experiment with new combinations. Your awesome new build may be perfectly legal, by both the letter and the spirit of the rules, but if you can't clearly explain it works--or how in the heck you got such a surprisingly large attack or damage bonus--then the GM and other players will quickly lose patience with your shenanigans.
I've found this to be a chronic problem in organized play, especially among players who rely too heavily on a program like Hero Lab to build their characters. Hero Lab is a wonderful tool--I use it all the time myself--but it's far too tempting to use it as a crutch for actually reading the rules. It doesn't contain the full text of every rule it employs, it doesn't always tell you where all the numbers come from, and it is far from error-free. Organized play campaigns usually have strict rules about owning a sourcebook in order to use its content, and a Hero Lab data package does not count for that. In addition, not all players have the time, funds, or inclination to acquire a library as large as yours might be, so you will occasionally get a GM who has never read the book(s) your character relies on for their core concept. If you can't adequately and efficiently explain that unfamiliar content to them--or can't account for each part of that surprisingly large bonus you just claimed--your GM will get frustrated with your poor grasp of the rules. They may even suspect you of cheating. Pathfinder Society has an audit process that GMs can invoke if they suspect cheating, but they don't do this lightly because it wastes valuable play time, and ruins the fun for everyone at the table. But if one player is stopping play frequently to fumble over explaining how their bizarro character is supposed to work, that still wastes the other players' time, and their goodwill.
The best way to avoid annoying GMs in this way is to carefully review the rules for your character until you can quickly and concisely explain how their abilities work. Be prepared to show the GM the original rules text if they request it, and to account for all your math in calculating your bonuses. If your character will be consistently creating effects that help allies or hinder enemies, be able to recite those effects quickly and clearly. Better yet, copy the pertinent details onto index cards that you and the other players can use for easy reference at the table. If you make a good-faith effort to keep your PC's unusual game mechanics from becoming a burden on the GM, they will be much happier about having you at the table! (Or, if those rules are overly burdensome on you, then you may wish to rethink whether you can actually play that character effectively.)
The player who doesn't pay attention to the game except when it's their turn, so the rest of us have to waste a lot of time telling them what's happened since their last turn.
Almost nothing irritates a GM more than being ignored, yet players constantly engage in pointless table chatter, playing games or surfing social media on their phones, and many other distractions. The worst offenders have to be yanked back to attention when it's their turn, then have the entire past round since their last turn explained to them, and immediately lose interest again as soon as their turn is over. They also never look at the [bleep]ing map to see where their character is in relation to their allies or enemies, which means they waste even more time deciding what to do on their turn.
(I should pause here to confess that I'm as guilty of off-topic chatter as any of my players, but that's a very minor offense compared to the sheer stubborn obliviousness of some people I've played with.)
I've considered banning phone use entirely at my table, but I'm afraid that would ultimately hurt the game more than help. The internet is often the easiest and fastest way to look up a rule, and some players keep all their character sheets and rulebooks on their phones. I also like to take pictures of cool maps and miniatures during games that I play or run, and I appreciate others wanting to do the same. But lingering on social media for longer than it takes to post those game photos, or playing games completely unrelated to the one we've all gathered for, tends to erode my patience very quickly--especially if the player is distracting others with their antics.
I understand that some players focus better if they have something to do with their hands when they're not taking notes or rolling dice. I have many friends who cross-stitch, or knit, or draw during game. I don't have a problem with that, as long as they are paying enough attention to know when they need to pause their project to take their turn, or roll a save, or otherwise react to what's going on in game. But if your crafty thing is too noisy or takes up too much table space, or if it takes effort to get your attention when I need it, then we have a problem.
Ultimately, I see this as an issue of mutual respect and common courtesy. If spending time with these people and playing this game is important to you, then show that through your actions. Pay attention, and practice active listening. Use the other players' turns to think about your next turn, so that you'll need less time to deliberate over your actions then. If the group wanders off topic, help the GM nudge them back on target, rather than providing yet another tangent.