Quick question: i accidentally plugged the negative wire into the positive plug on my battery (also positive wire into negative plug). When i turned on the car, my capacitor on my esc smoke a little bit. The battery then stopped working. However, i put a new battery and everything worked fine.

Do you think my esc is ok?

Thanks

Probably but you may want to replace the esc cap to be on the safe side.

Do you think it would be bad to continue running my car?

Depends on the ESC, some work Ok w/o the cap, some risk damage without it. It's a cheap fix, probably available at your LHS so you wouldn't even have to order it.