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So I'm about to finish making a vocal booth out of 4'x2' Bass Trap panels (homemade) stacked up as the walls and ceiling (Basically it'll be a 6.5' tall 4'x4' box). The whole thing cost me around $500, but I'm wondering if there will be any more acoustic issues I should worry about.

I want a completely dead. Will the bass trap panels bounce any high-end or mid frequencies back into the microphone?

Bass Traps are broad band absorbers - they are only called "bass" because they are thick enough to have some effect on bass frequencies. They actually absorb highs and mids more easily. Absorbers won't reflect much of anything, but your outer room WILL.

Maybe surround a speaker with panels and listen outside - that will give you a rough idea of the amount of sound energy available that is being reflected back to the booth from either the room walls or the walls or frame of the booth (if it has any) . Resonances have bitten me in the past - there was a ringing when a guitar or vocal got into a certain range and volume and the only solution was to change the mic/booth location.

No expertise implied.

You may theenk you want completely dead, and if that's okay for you, it's fine, but singers tend to be uncomfortable in totally dead rooms, cuz who sings in a closet? I use a folding room divider hung with a thick duvet (no top) with an inexpensive reflection filter mounted behind the mic. I can position it front of an open or closed clothes closet, or a bookcase, (if I want diffusion, rather than absorption) or open it to the room for more distant space behind the singer. The main thing is to pay attention to the rule of thirds when positioning the mic, so you hopefully don't have a massive hump or dip at the mic position. I start at a position a third of the length of the room and a third of the width and adjust from there; the midpoint of any two room boundaries, (including floor to ceiling) is what you want to avoid.