FWIW, I've now had 5 yrs of experience with clover plots. I've gone to mowing the clover less frequently than before, and now do so only twice per season, with the second mowing sometime during September, coinciding with my last fertilization.
I believe there is some benefit to getting the clover plants to more-or-less complete their life cycle, by flowering and going to seed, and this is best facilitated by fewer mowings. I didn't come up with this on my own, a wise man explained it to me.
Two mowings seems to be sufficient to control weeds. However, my bigger enemy is invading cool-season grasses; as anyone with a lawn knows, mowing and fertilizing is a practice that favors the grasses.
Incidentally, some weeds ("forbs") are not necessarily bad in your clover plot, particularly if you stay with your fertilization program. One particular forb that appears on my farm, commonly known as Winter Cress, is a notably preferred deer food, besting even food plot plants at certain times of the year. Certain invading wildflowers are also aggressively browsed. Remember, deer have been enjoying forbs for a lot longer than they have the plants in our food plots, or even agricultural crops.
I've sometimes read that weeds/forbs are categorically low in nutritive value and palatability to deer, even from well-recognized sources. Absolutely, positively untrue.
If you have any "old field" areas on your property, and have the inclination, you can experiment to identify deer preferences of forbs. Mow some spots, to encourage new growth. If the mowed spots are loaded with grasses, spray with some Roundup (which is very effective on cool-season grasses), and see observe what kinds of forbs pop up. Then pay attention to the plants, and identify the ones that deer appear to be feeding on, at various times during the year (their preferences change throughout the year, influenced by plant maturity and the physical needs of deer). You might even soil test and fertilize your test area, which is likely to spark the deer's interest.
An aside on the benefits of soil testing and regular fertilization - I have a half-acre site in which I've now had a variety plots planted, and always fertilized it 1-2 times per year. In late summer 2002, I sprayed Roundup to the plot, in anticipation of a fall planting, which never materialized because of scheduling conflicts. The plot sprouted up with cool-season grasses and a variety of forbs. Deer were seen regularly in this plot throughout that hunting season; in fact, believe it or not, I believe that site got more attention from deer that year than it did this year, when it was full of a lush plot of Buck Forage Oats.
Incidentally, the aforementioned information about forbs is something you'll never read about in any literature from the Whitetail Institute or Mossy Oak/Biologic!