I recently had my left axle replaced, and the guy who did it must not have checked the seal where it connects to the transmission. I noticed a transmission fluid leak at this spot, it leaked out all over the underbody of the car and onto the catalytic converter. The fluid level on the dipstick covered just a tiny bit of the bottom of it. Would a transmission fluid level this low cause the transmission to be hard to shift -- i.e. it'll rev way up a couple thousand RPMs a few seconds until shifting into the next gear?

Fluids not being at their proper levels can cause all sorts of different problems.

Please fill to the proper level following the proper instruction about having the car running when you check trans fluid etc.

With not enough fluid the pump can starve out causing a drop in pressure. then the clutches can't engage causing slow shifts.