Just picked this xj up and it has a couple funky things going on.

Bought it knowing it had a very slow sluggish start..figured starter or battery. Auto zone says battery so I bought a new one..still not a zippy start but better

Soon as I swapped the battery in it idled normal for a few seconds then dropped to nothing and stalled. Started back up...same thing. Started 3rd time and it stayed running but the rpms fluctuated for a good minute..when you rev it it feels like the RPMs drop for a split second then revs

Drives fine....after I got it om the road the rpms seemed fine.

Also before I swapped the battery I was getting a cylinder 1 and 2 misfire..
Any ideas?

 

No one?

 

With the battery disconnected long enough, the pcm re learns the idle and running for the first while afterwards. Everything is adjusting under normal situations also but has to find its baseline after the computer loses its memory. What you noticed with the stall and idle is normal at first, but it should have straightened out most of the way by now. The misfire will probably show back up if there is any problem, but with the newer model like ours, plugs are pretty much the extent of our tune up. Worst case you may need a coil pack which replaces all of them in one part. They are very simple as far as the experiences you have mentioned