07 Sliverado miss fire following Transmission change out

I have a 2007 Silverado Classic with 4.3 V6, truck has 254000 miles. This has been a really good/dependable work truck. I recently blew the automatic transmission while on a long road trip. I had a rebuilt transmission installed while I completed the trip in a rental car. My problems since have been a strong misfire and now the tachometer is fluctuating all over place.
Neither problem were there prior to transmission being changed out both started as soon as I started home with new transmission. Transmission seems to be operating fine, shifts smoothly. The guys at the shop ran a diagnostic and say its #3 & #4 cylinders misfiring. I had a complete tune up done prior to the trip including plugs & wires. I have pulled all plugs and they all look brand new, no fouling.

Any ideas or suggestions?

A number of things could have happened during the trans replacement, and of course there is always the random possibility that it is a coincidence and the trans job had nothing to do with the misfiring.
I would take a close look at the electrical plugs on the injectors, as well as the coils/plug wires, to see if any were damaged, or got partially un-seated.
Next, I would recommend you take it to AutoZone or one of the major parts chain stores that offer a free scan, and see what their specific trouble codes are, then post up the codes on here. Several really good techs will share their advice and experience on what your next steps should be.
Some of those stores will also give you a printout that lists the probable causes/potential parts to replace, but don't immediately buy any parts based on those recommendations. I recently replaced a $2 rubber O-Ring seal on a pickup, (where the EGR pipe enters the intake manifold). The guy had already bought over $150 worth of sensors and other suggested replacement parts. The vacuum leak from that bad seal threw codes for Lean Conditions on multiple cylinders, and it was misfiring, and idling like junk. He was happy to pay me $50 labor and go return all those un-needed parts for a refund.

Thanks for the quick response, I'll get the codes and take a look for loose connections. I'll post any findings and codes.

So the error codes are:
P0300 random misfire detected & P0751 shift solenoid A performance or stuck off

I’ll get the electrical connections checked out this weekend

I don't know what the Shift Solenoid A controls, but you said the new trans seems to be operating normally?

The P0300, I would say random misfire can be more challenging to troubleshoot than a single cylinder misfire, although it is "usually" something that can be fixed easier than, say, a cylinder with low compression, valve train problems, etc.

Gotta ask, (because I haven't worked on any 4.3's newer than early 2000's), is it a single coil, or one per cylinder?
Also, what brand and P/N spark plugs did you have put in it during that tune-up? (Again, don't know about your 4.3, but the LS type V-8's are very particular about spark plugs - They definitely prefer Iridium plugs, which are kind of spendy, but they last 100,000 miles and do not misfire unless there are other issues).

One more thing you might do this weekend - check for any vacuum leaks. They can cause misfires, and often do not illuminate the check engine light.

The 4.3 has a single coil. As for the spark plugs, I’ll have to double check but they are the same as the originals. This was the second time the plugs were changed. I still had the original plugs in my tool box when I was checking them earlier.
The tranny is doing fine, there is a slight growl with the new one but seems to be doing fine. I am hoping to find a connection loose. Do you think contact cleaner would be beneficial?
I have run two tanks of gas with injector cleaner in case one of the spider jets is plugging. No help.

Here are some of the more common "potential" causes of P0300 on a Silverado:
1. Vacuum Leak
2. Spark Plugs, or Wires
3. EGR Valve system, (including any leaks in the exhaust tube routed to the intake)
4. Incorrect Fuel Pressure (high or low)
5. Fuel Injector(s) or associated wiring
6. Ignition Coil (less likely, but possible).
7. Low compression (again, less likely, but a possibility).

Most of these can be easily inspected, and tested. Especially if you have access to a vacuum gauge and compression tester, (they are both fairly inexpensive these days, and readily available - Harbor Freight has decent ones for the $). You can rent/borrow fuel pressure test kits from O'Reilly or AutoZone. Visual inspection can spot things like a loose injector harness connector, or help identify possible vacuum leak, etc. Since the problem popped up after your trans was replaced, pay particular attention to things that could have been knocked loose or damaged during that work - like pinched or damaged vacuum hoses, wiring, loose connectors, etc. (Double-check the ground straps got reinstalled - bad grounds cause more problems than most folks would imagine).
(Google and YouTube can be helpful, but use common sense and think Safety - Spraying any flammable liquid such as starting fluid or brake cleaner is not such a great idea if you have any external sparking going on, etc).

I’ve been at it most of the day, here is what I have found...positive battery cable slightly loose, while checking electrical couplings at tranny one made a click sound (hoping it wasn’t completely plugged in), found open ended hose near rear of tranny.

I tightened up the battery cable. I have searched but do not see anything that hose could attach to, it is secured to one of the wiring harnesses with about 4” free. It comes from above transmission, toward front of truck. I can’t see wher it goes to. Test drove truck...same as before.

All plugs look good, all plug/coil wires are in good condition and solidly attached. Plugs are Iridium. Tune up done in August included new plugs & wires, distributor cap, air & fuel filter.

Talked with the shop that did the transmission change out. Came with new shift solenoid A & B, cooling lines were flushed, there were no vacuum hoses to tranny but there is a vent hose.

with that mileage the distributor requires replacing and I would also replace coil.

fuel pressures test is required key on eng off 60-65psi..

hose on tranny is the vent hose so if not connected sloppy work.. solenoid coil code again they screwed up .. usually DIY will put pan on and mess up those solenoid connections .. these are located down low on the rear of the pan install. also they could have damaged the wiring/connector on the tranny .

good luck .