For one or two issues that can easily be corrected (i.e. missing cookware, need a new bedspread), a call directly to housekeeping or maintenance is normally sufficient. I've had to do this a number of times myself for everything from missing dishwasher detergent to a leaky dishwasher, and have ALWAYS received a prompt response from the staff.
For issues of the nature you describe, I would have made a list and taken it to the front desk personally. Discuss the list with a manager, give him/her the list, and establish expectations for getting the items addressed. The manager may immediately suggest switching your room or offer to have the problems addressed. Except for the carpet, all of the things you mentioned should be fairly easy to correct. If your intention is to immediately head out to the parks, then I would think it reasonable for the manager to offer to have the problems addressed while you were gone.
For what it's worth, I would never suggest calling the "front desk" for these sorts of things. Disney resorts actually use an off-site call center to handle calls to the "front desk." More often than not, there seems to be a communications breakdown between the call center and resort staff. Your list of problems may never even get into the hands of the manager or anyone else able to help.
I have mixed feelings about writing letters. I would never directly tell someone NOT to write a letter, but I do question how much action Disney / DVC takes in direct response to such letters.
In this case, the bottom line is that a letter would do nothing to fix your stay. Better to suffer a few minutes of aggrivation in dealing with a resort manager than to have a miserable trip due to the uncorrected issues. If you HAD reported these problems, the resort staff may have immediately redeemed themselves with a positive response. Now they don't have that chance.
(And here I go, ranting again!)
IMO, better to rant and benefit from others' experience than to sit unhappily on the sidelines.
