1. He enters dungeons (Illusion Barriers) without his consent.
2. Too many pop-ups at a time could distract him in fights (applies in some games as well).
3. Difficulty in controlling his strength - Normally one can control his/her body's strength, however, in his case as he masters his passive skills then the damage he inflicts would also be passive. What if he tries to punch a normal person? Even if he holds back, his base damage wouldn't change (like punch base damage = 50 and held-back punch base damage still 50 unless he learns a skill like "held-back punch").
4. Triggering undesired events (like the appearance of the Legion Zombie).
5. Combination of game varieties. Currently, we see "The Gamer" ability as that of an RPG. However, that doesn't necessarily mean it would only/always apply to that. It's possible that other kinds of games would also apply to his ability (he mentioned a lot before about martial arts games). What if some other games such as Eroge apply to him? Sounds like a benefit, right? But what about its bad ends? You could get killed by a game's story progression no matter how strong you are. And if story progression does apply in his ability, then events will unfold in front of him whether or not he does anything.
6. Lag, bugs, disconnection, patches - I know they're technically outside the game, but what if those actually apply as well?