1996 Nissan Pathfinder V4 Engine - Distributor - Bullet Hole?

My nissan pathfinder runs choppy. It’s an automatic but acts like it’s a shift and I don’t know how to drive a stick shift. The mechanic had a hard time diagnosing the problem but eventually he said it needed a new distributor. Replaced the distributor and it helped but car continues to act up–just not consistently. For the last two days, I’ve recorded, the time of day, miles driven and the rpms. Other than the fact that the problem kicks in at between 150 and 200 rpms there’s no rhyme or reason on when it acts up. However, the second time I picked it up from the mechanic, I drove it 15 miles without a problem. I parked it in an underground garage for 3 hours. I then drove it home 5 miles and a ten minute trip took 35 minutes because of the bucking. My mechanic is at his wits end–as am I.

I’m sure this isn’t related, I noticed a bullet hole in the front upper panel above the tire well a couple of weeks before this problem began. The mechanic found the bullet but no other damage was noticed.