I think sometimes the "month" is staggered; some people pay their rents starting from when they move in rather than the 1st, or, if one moves in other than the first of the month, that is pro-rated; so you tell the first place you are leaving Saturday, August 31, but you get the key to your second place August 21st or something?

Yuck on the fridge! I always have bath mats anyway so I would put up with the bath strip glue marks but it would be a bit depressing; using a refinishing kit though would make it look like new I think, if they are any good at it. With the fridge I would just report it is not working "right" the first week (funky smelling is not right :-) their maintenance people can't really fix refrigerators so they'd swap it out? Or, if you have to pay a security deposit on the apartment, just point out, "Hey, I'm paying a security deposit you'll get interest on for the next 25-30 years, how about a new fridge?" It makes it sound like you are interested in staying forever and want to be treated as a friendly, loyal, customer.