You can't really mow clover too much - it wont hurt to take it down 2-3" several times per year.
Here's a 2year old plot - with the 1st mowing this June (Jun15th) - You can see this plot has some weeds (Daisys, ragweed, paintbrushes, some other annuals and some grasses. The grasses are what you need to worry about most - don't let then go to seed - and spot treating them with round up is a good idea (I almost never have time though).
I'll post this plot pictures in a week or two - and you won't know there were any weeds. The clover can really dominate once established well.
FH