If you have the slightest doubt, leave it.

It could also be candle smoke if the previous tenants burned many of them. Smoke tends to be distributed like you describe, mold damage is patchy and follows the path of water trickling.

Take a ladder in and rub a white cloth across the suspect area ... smoke rubs off easily because it's on the outside of the paint. Mold damage is inside the wall and the staining doesn't rub off much.

Sushipup-great advise...but trying to see if it needs serious help or if it is something different.
Lazygardens-Thanks....this is in a lot of the rooms and all basically at the top of the walls and the abutting ceiling area. It isn't the dark black spotchy that I would suspect of mold...but like someone took some dark grey watercolors....if that makes sense?
Any other ideas of what it could be?

Smokey fires in the fire place could cause it

Or if you are in a "420" friendly state it could be a different kind of smoke

Hippy! I totally had to look up what 420 friendly meant! We are in Nebraska, which is currently going broke keeping cops at the Colorado border! No joke.

It sounds like what is often called "ghosting" or thermal tracking. There are a few other names for it, but it's often mistaken for mold. It's related to temperatures, and can be caused by air leaks in a home. As someone suggested it can be soot. It might also be simple dust/dirt built up over years.

This site has a pretty good explanation:

Here is a link that might be useful: Thermal Tracking

Rrah- Thank you so much for the article. I am most certain now that while there may be mold somewhere, it is not where I am looking at the markings. It is definitely caused more from either thermal tracking, candles, or some other sort of air circulation issue. The furnace was recently replaced, so it was probably bad for some time.

IMO, signing anything for a rent to own without doing a home inspection first, would be a big mistake. Why do you think it cannot be done prior to moving in? In fact, you should get an appraisal, too. Check into the sellerâÂÂs mortgage status and financial strength. You actually need to do more background checking for a rent to own than for a typical purchase, since you will be working under a long-term contract with the seller.

Renters can certain expect their landlords to test for mold and remediate it.

I realize you have probably figured out what the problem is and it it's mold. But do be aware that landlords usually have to make sure a rental unit meets certain criteria, and not having toxic mold is generally one of them.