MechaPilot
Explorer
As for races, the only thing I disallow is flying races. I can imagine that being abused and, most importantly, splitting the party.
I have been allowing flying PCs for at least a decade now. In my homebrewed Tenesia setting, arcane casters can fly on brooms as long as they have spell slots remaining (Actually, the rule is spell points remaining, Tenesia uses the spell point variant).
From my experience (and mine is certainly not the only one, so I'm not claiming some grand authority to declare this) flight is pretty hard to abuse, especially in dungeons which are prone to having relatively low ceilings, and especially if the flight is winged. I have a rule that if you are a winged flier, you cannot fly unless you have room to spread your wings. For a medium-sized humanoid, I assume that means each wing spreads out into an adjacent 5 foot space. So, in my games, a medium-sized winged flier can't fly through an area less than 15 feet wide.
That said, flight certainly can lead to party splitting.