Probably stating the obvious here but your going to continue to have this problem until you install some drainage that directs all that water from the downspouts and any residual surface water, to the street (pop up drainage emitter near the sidewalk).

I also pay attention to things like the outside, the sidewalks, and who's living there.

Hire at least two different inspectors.And the sidewalk became an issue.

Can pedestrians walking by see it from the sidewalk?

I think we need to do more to help the make our little part of the world better-help those who are less fortunate and struggling to have a better life even if it is something that may seem minor to you or make someone's day better (buy the person behind you in a line up a cup of coffee, shovel someone's sidewalk in the winter).  

For example, you lease a home to someone who has a guest who punched another guest causing him to fatally his head on the sidewalk.

I have a house where the neighbor had 2 driveways, one driveway even had the matching sidewalk going to my house-- but legally it was theirs.     

2) Who's responsible for keeping the sidewalk and 18" of the street clean?

Timing or not, I wouldn't sign a lease in my personal name, you have little to no protection in the event there is a liability issue - ie grandma slips on the sidewalk - under LLC they have to sue the LLC if that's where property is owned and the lease is drawn. if it's owned personally they can sue you and everything you you have. bottom line is I say delay and get an LLC but that's just me

Don't forget to clean your driveway, sidewalks, and any other hardscapes while you're at it!