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.