It is left largely unclear if the bullet had any actual physical or mental consequences for Bazil. But there are situations when he seems to lose it a bit, especially in situations of stress:
- There are times when he stands rather sunken in his thoughts imagining weird things. This happens for example when he's discovering the two arms dealer factories and imagines the dramatic soundtrack actually played by a real orchestra, or when he tracks down one of them in his car and imagines a weird landmine-spiced football game.
- Other times when is under stress he has to calm himself down by reciting weird trivia facts in his mind, like when he is eavesdropping as a living hallstand, when he's on the roof and fears for La Môme Caoutchouc's well-being, or when he's kidnapped by the arms dealers.
- And other times under stress he seems to develop a very nervous twitching reminiscent of an epileptic attack and needs to be called to reason by himself or someone else, e.g. when he gets into arguments with La Môme Caoutchouc (though, in one of those he just pretends for humorous effect) or when he's threatened with a gun.
Now those are pretty weird traits of Bazil's character and they might very well be caused by the bullet in his brain, especially the quite physically seeming situations described in (3). But the unfortunate truth is, we don't really know. They might as well have always been part of his character and his stress-management or part of Jeunet's eccentric filmmaking in general, especially the rather figurative imaginings described in (1). This isn't helped by the fact that we don't really get to see that much of his character before the bullet incident.
But we might also be able to extrapolate a little more indirect psychological effect on Bazil and his attitude towards life. When they're operating him in the hospital there is a discussion similar to this:
doctor: If I remove the bullet. he'll only be a vegetable. If I leave it in, he might drop dead at any moment.
assistant: It's better to live with the chance of dropping dead at any moment than not even knowing you could drop dead at any moment.
Now it's not that Bazil seemed to be a particularly active and productive person even before his accident, but it might very well be that this incident and the chance of dying at any moment might have even loosened his attitude towards life and achieving something higher and maybe also his fear of death. As when asked about his goals in life he says something to the effect of:
I live from day to day. With the bullet in my head I could lose it at any moment.