Well, some of the bard's power comes in the form of inspiration dice (or their opposite, cutting words). Depending on the playstyle of your group, these can be more or less powerful. If you are a group where all dice are rolled in the open and you take a little time to 'calculate' the results, then inspiration is 'balanced' as that is how the rules describe it working: You can chose to use the inspiration dice after the d20 is rolled but before the result is calculated.
If, however, you and your players possess a basic competence in math, such that the 'result is calculated' pretty much simultaneously with the die roll, then inspiration and cutting words can be a little more powerful, as the players will chose to use them only when the extra die actually has a chance of affecting the outcome. Is it game breakingly OP? Not in the least, but it is certainly more powerful than the alternative.
As for anything else bard related, unless your player is also talking about multiclassing in some way, I'm not aware of any 'gotchas' in the bard class beyond the nuances of inspiration. They get a relatively small selection of spells with some overlap with the wizard and cleric, allowing a bard to partially fill either roll. They also have some unique 'bard only' spells, but nothing blatenly OP that I've observed in play. The only thing I'd caution you to watch out for is not specific to bards, but just to spellcasters in general, and that is to make sure you understand what spells are concentration based and which aren't, so that you don't have players stacking spells inappropriately.