Take a deep breath when you walk in a place. If it smells musty or damp, there’s been water damage or mildew issues. Check around windows for signs of mold, as thats one of the places it tends to happen in older homes. Old windows = moisture issues. bugs can get in around windows too, make sure they are sealed properly, and hopefully with screens on them for when you need to open them.

Well, number one make sure the a/c cools down really good :~)

Probably most homes in the world have had water damage, it’s making sure they’ve have mitigated it properly….you would most likely find this around the a/c unit as that is where mold seems to usually happen. At least that is what started this big mold fiasco in Texas.

Windows are important – make sure they open and close and it’s true what Monkeybun says, if the owner doesn’t properly maintain the home.

I think even more important that what’s wrong is how the landlord intends to deal with problems as they come up. You need to get, in writing, a promise for response to issues within 24 hours max. You also need written promise that the landlord will pay for all repairs, parts, etc. at time of service as required, not “you pay and I’ll pay you back”. Or, at a minimum, agreement to keep receipts for records, approval (initialed or by phone and noted immediately after) of work and costs, then taking that amount off your next months rent as way of reimbursement.
Look up the landlord online with the Better Business Bureau. Someone once suggested stopping by the local police and asking if they ever had any problems at that residence or with that landlord. You want a responsible, conscientious owner, not a deadbeat or crook. And you want to be very careful who has a key to the place. Possibly put in writing that you will only allow entry if you are there at the time, except in an emergency (with Police or Fire Dept. along to get in.)
I rented from a good friend last year, and it took a lot of the worry out of renting from strangers.