last summer I used my car every day for about 3 months, driving from house to house to house to B&Q to house, all a mile or two distances at most, working for a landlord who owned a load of properties i was doing work on. Wasn't too bad on the economy, and I can't think of any other problem you might be thinking about.
My daily commute is only 6 miles and I don't do many longer distances other than proper trips, i.e. 80-120 miles each way. So most of my driving is short trips, and it's never been a problem.
And yes you're right about the syncrho issues, though they don't occur in every pre.