It depends on how nit-picky you want to get on a mobile home.
You could call out:
open risers
a non-graspable handrail
failing paint/stain
poor connection of stairs to deck (I don’t see stringer hangers or a ledger, appears to be toe-nailed looking from TN)
riser height varies more than 3/8 " (look at that big bottom step)
riser height more than 7.75 inches
weak handrail (no newel post) as you already mentioned
stringer spacing depends on the tread material. For some types of composite it is a little as 10-12" (manufacturer instructions). I agree 16" for 2x12 treads should be fine.
deck sagging.
grade appears to be pitched down toward deck so water might accumulate.
That’s all I have from here. There is probably much more you could point out if you want to go that way.
One does not need a post at the bottom of the handrail as long as it can withstand 200 pounds of horizontal force…BUT it does need a graspable hand rail and a 2x4 is not one.
The black substance looks like what is on the ground. Maybe that area of bricks was wet when they moved the ground cover around?
I am going to thank guess at this not knowing if that is a driveway or not and say that someone backs there car into the driveway with the exhaust blowing on the brick skirting letting it idle for a period of time leaving black exhaust stains.