I'm guessing that you have a 2nd generation MINI with the apron or cowl pieces at the base of the windshield. These Apron pieces has the rubber seal molded to them, that seals against the windshield - and they deteriorate over time. The only solution is to replace the entire apron / cowl pieces, right and left sides.

The failure of the rubber seal is not a critical item since even if they leaked water, the water will not enter the cabin.

Yes, the dealer can repair this.

I'm not familiar with the 08 or later MINIs but modern windscreens usually sit on top of the steel body with a full bead of sealant under the glass.  Original minis suffering cracked screen seals with water entering the cabin can be remediated with black silicon sealant forced under the seal on the glass side. I usually would go on the two sides and the bottom edge as water will run downward. 

I'm sure the dealer will be glad to take your money for a repair.

I just purchased a 2008 Cooper S and I am going over it, noting issues and things I want to do. One of the things I noticed today is the rubber seal and plastic trim (for the windshield wipers) is cracked and pieces of the rubber are breaking off. How much of a concern is this and is it something that can be fixed by a dealer? Thanks!