Yeah, like they said above, such a broad term and comes down to the person doing it, so if you seek that service from an individual ask what specifically will be done. For some its taking everything off the top of the playfield, cleaning it and replacing all rubbers. For some that includes taking everything off of the top AND the bottom and cleaning it and replacing all coil sleeves. For some it may mean rebuilding flippers, for some it wont. I never really trust that term when looking at a pin someone is selling, I ask specific things. Heres a quick list of what to ask when buying a "shopped" pin or having someone "shop" out your pins:
1. Will you be taking everything off of the top? What do you automatically replace? All rubbers, faded posts, do you swap out all bulbs for new ones and will those new bulbs be LEDS? How will you clean the playfield, will it be waxed?
2. Will you be removing everything from under the playfield? Washing the wire harness? Replacing all coil sleeves? rebuilding flippers? washing all of the mechs? Changing all bulbs under playfield, using standard or LEDS?
3. In the back box. Will you be checking all of the fuses for correct values? New Batteries? Will any burnt connectors be replaced? Changing all bulbs in backbox?
To answer your original questions, I don't know if they would fix those things you mentioned. As far as the left flipper not coming to a full rest, consider doing a flipper rebuild, its inexpensive and helps a game play better than ever. Check this link out:
If that seems too daunting, just take the plunger out that goes into the coil, clean it really well with something like Purple Power or other type cleaner, and put new coil sleeves in it, they cost less than a dollar.
For the batteries, I would look into removing that battery holder and putting a new remote one on it. Do a search on here and you will find lots of options.