Hi everyone,
New to this forum, and am looking forward to reading through post to find useful info.

My immediate problem is with my 89 Buick Lesabre Limited 3800, I recently bought it from my parents, I moved back to my home town in Oct 2012 the car had been sitting in garage for 5 yrs and was never started. From that point i have been starting it up after putting a battery and fresh gas in it, and letting it run up to running temp. several times a month. It ran great with no apparent problem even though they had stopped driving it because of a plugged catalytic converter. As i say it seemed to run good, until a wk after i bought it in Dec 2013. I hadn't registered it or drove it on the road yet when the ck engine light came on, since then its had some problems. since then whats been replaced by qualified mechanics is: Catalytic converter, ECM, ICM, Cam position censor, EGR Valve, Trans vacuum modulator and a injector wire repaired. The common problem that has continued is and all these other fixes where suppose to fix is, after shutting it off for 10 min to anywhere up to several hrs, when restarted i can put it in drive and it will run fine until the first stop at which time it starts idling rough and has no power until it gets moving with some RPM'*. once it gets back up to running temp it runs great. It some times backfires into the intake if i keep depressing the gas while its bogging down, the only code that can be gotten is an old history code 48 for misfire, but the ck engine light does not come on anymore, that stopped with the EGR replacement which is the last thing that was done.
Any ideas would be appreciated.

Kinda sounds like a vacuum leak, kinda doesn't. With it sitting for 5 years there is a good chance some (if not all) the rubber vacuum hoses have dried up and cracked. I would replace them.

I have already ck'ed and replaced as necessary the vacuum hoses, air filter and fuel filter. Sorry i forgot to mention these things earlier!
It also had wires and plug just before it was parked.
The car has 95,000 original miles.

has this mechanic checked fuel pressure? able to scan for fuel trim on obd1? kinda seems like injectors are dirty and rich, that would explain taking out the cat

He had a scanner on it, im not sure what all he ck'ed. i know he mentioned at 1 point he saw a spike in rich mixture, that was the first time he worked on it. He'* a retired 35 yr GM mechanic and i believe he is plenty capable, but at this point he say'* if the lights not on he'* not doing anything with it. I dont think he wants to spend his time tracking down bugs in a 25 yr old car.
The other day i put a screw driver on each of the injectors and 1 sounds alot different than the others, the click is not as distinct in it.

im not sure on a 89 what they look like but some you can take off the rail, and then reassemble over a bucket or something and crank the engine and see what the spray patterns look like. they have testors that can flow test it but i havent had to have one done so i dont know if its worth it over getting new or junk yard ones

Im not sure its an injectors problem, it only acts up under specific conditions.