Handyman filled with an insulation strip and drilled one ugly piece of wood to cover the largest gap on the top, and called it good.  

Liability can then be limited to each "cell" and the owner of any cell is insulated from activities of other cells, state dependent.

Also, blown in insulation is pretty inexpensive.

The doors were insulated steel, and were pre-bored with 2 holes.  

If temperature differential is greater than 14 degrees, and you have proper airflow,  you might have an issue with your insulation, or air leakage around windows and doors.

Since we declined to renovate the basement the tenants now want to put down a roll of carpet for some padding and maybe hang some nice fabric on the walls to cover the insulation and wood studs so that they can create a little play area for play dates at their own expense.What do you guys think?  

This is super important because if you miss on point #1 above, you still have a "buffer" to insulate you to some degree from short term market fluctuations.3)I ALWAYS make sure financially I can easily afford to hold the property through thick and thin.

We really care about green apartment living, and try to attract green-minded tenants with good insulation, energy star mechanicals, solar panels, and a tilled garden bed ($30 well spent!). 

Some of the older buildings have cheap insulation that is in the ceiling and walls.You can almost hear every sound in the other unit.

It already has the vapor barrier and sound insulation and sells for about $1.80 a foot.