Once the previous tenants painted the paneling, what was once a maintenance-free wall is now on a maintenance plan. (It makes you wonder why people paint brick, formica, and vinyl flooring. Geesh!!!)
Anyway, the 'fix' is NOT gonna be pretty. In fact, if you don't get it right, you may end up doing it again. (If I was you but I'm not, but IF I was, I'd rip out the paneling and install drywall.) If you want to repair the damage, first, I'd talk to the landlord. Make sure you have his permission. He may want to have one of his 'pros' do the job. And after they're finished, get some sort of doorstop! There are a variety of stops that are in the Hardware Section of Home Depot, and such. (Check to see if you need more stops at other doors.)
BUT, if you insist on doing the fix yourself, I suggest you get a piece of replacement paneling that's 4' wide and about 1' higher than the doorknob in length. Remove the portion of the wall that's the size I just described. (Ooops! Do the removal FIRST because paneling comes in different thicknesses. THEN, go buy a 4x8' sheet for your job, and THEN cut it the exact size of the piece you removed.) You'll need nails, spackle, a spackle knife, 220 sand paper, and a couple of unmentioned tools. (You'll need to remove the walltrim too, if any, to remove the damaged piece.)
Install the new panel. Take a wet sponge and 'lightly dampen' the new piece. Then apply joint compound in the crevices and at the seams at the sides AND at the horizontal seam. Let dry and sand smooth. Apply another layer of compound, let dry, and sand again. YOu keep adding a little compound at a time until the wall is completely smooth. Don't worry if it takes you 10 coats to do. And don't worry if you sand off too much compound. The nice thing is you can add, and remove, as much or as little compound as you like. Really, you can't mess this part of the job up.
Then, you'll need to apply 2 coats of Primer/Sealer. Buy it at a Paint Retailer; NOT at Home Depot. (Look in the Yellow Pages under PAINT - RETAIL.) Apply 2 coats of Primer/Sealer. Tell the Retailer what you're Sealing/Priming. Then, apply your topcoat. Plan on 2 coats. Buy your topcoat of paint at the Paint Retailer too. Be sure to read ALL the instructions on the cans of spackle, primer, and paint BEFORE you leave the store in case you have any questions. Also, while you're at the store, when you tell the Assistant what you're doing, be sure to ask what tools you'll need. That way, you're totally prepared. Oh, if the dust from sanding is a problem, you can use a DAMP sponge to 'smooth out' the dried spackle. If you do this, then DON'T go crazy applying a LOT of spackle in one coating. If you do this, your spackle will crack. Do a little at a time, in layers! When you're ALL finished with the spackling and sponging, THEN do 1 light sanding. That's all. DON'T re-sponge.
I may have missed something in this process. Hopefully, others will add to (or take away from) my post. I'm in a good moood today so I rambled on a lot. If you need more info, post up (perhaps w/a new question.) My best to ya and hope this helps.