Does a diacetyl rest for a week or more adversely affect the beer in any way? With our busy lives it's easy to forget about a batch for a few days (especially when it's in the dark recesses of a cellar).
Not really, no. If you're doing a beer that has diacetyl as part of the flavor (such as English ales), then you might find that flavor missing, or lessened, in the final beer.
The one thing to watch out for is leaving the beer at high temperatures for longer periods of time. The higher the temperature, the faster the settled yeast will begin to contribute off flavors to your beer. I can't see one week at diacetyl-rest temp being a problem, but 4+ weeks at 80+ degrees and you'd probably start to notice a problem.