Paying higher closing costs, or points, may or may not be a good idea. It all comes down to timing... if you pay points and don't stay in your home for very long, then it may not be a good idea. You can check this out by comparing your mortgage payment (without PMI, insurance or taxes) with and without the rate reduction that you'll get by paying points.
If your payment with the lower closing costs (no points) is $1500/mo and your payment with the higher closing costs (points) is $1400/mo, then you have $100/mo that you are "saving". If the points cost you $2400 up front for this interest rate reduction, then it will take you 24 months to break even, and after that you'll be receiving the benefit of the $100/month difference. With these assumptions and also assuming that you stay in your home for 5 years, you could save $3600 by paying points up front.
Interim interest is the prorated amount that is due between the time you close escrow and the time your first payment is due. PMI is avoidable with certain loan programs, but if yours is requiring it then the rate is normally not negotiable.