First you never accept check.Ask for cash for first month, last month and security deposit.You save headaches by doing this.
Screen each applicant very cafefully. Make sure he or she has an income of 3 times monthly rent;otherwise do not rent to that applicant.If you do this , you know tenant will have money to pay rent. Run credit report to see if the applicant is a good payer and does not have too many charges and other bill pending. This is the best way to do business. If tenant move out change the lock and save any documentation you served to tenant just in case of reclamation. We learn by making mistake but do not do it again.
There was good advice for choosing a new tenant. In your case If you went into place & nothing was tore up I'd change the locks - but make arrangements for her to take property (I would be there at that time to keep an eye out for damage) & check at the end. I'd count this as a learning experience. It would be a real hassle to go after the person & they obviously can't or won't pay bills. Also, I would check to see that she'd not left me holding the bag for any utility bills - but since it's such a short time if there is cable/phone,internet - they better all be in her name not LL.
Utilities - I'd probably not worryl. I always check to make sure Tenant has changed them into their name before they move in.