I fish with braid on some rods (usually have 4 or 5 to choose from on the boat just for me). Problems arise while fishing also, but a little extra care cures most of them. Some suggestions I've seen are to use a candle to wax the line...stiffens it up a little. Others suggest using line conditioners like fly line treatments or KVD Line & Lure Conditioner.
http://www.tacklewarehouse.com/Kevin_VanDams_Line__Lure_Conditioner/descpage-VDLL.html You can get it at Bass Pro Shops or Cabela's, if you have one close to your location, but Tackle Warehouse has a more thorough description and customer reviews (all very enthusiastic). I have not used it yet, because I have "Blakemore's Line & Reel Magic" on hand, and it works very well, tho haven't used it on braid. I had a guy in my backseat once complaining that he couldn't cast far enough. I sprayed his line and reel down with "Blakemore's"
and his next 3 casts were onto the shore. I think he was impressed, 'cause I was! Another tip would be to try Power Pro "Slick" braid. Has some sort of coating that makes it a wee bit stiffer, from what I've read. Generally, being more careful is still a requirement.
I like the old fashioned 7-strand stainless cables and see no reason to change. Tom Morris seemed shocked and dismayed that I didn't want the 19 strand lines last time I ordered lines from him. Everybody seems to think that the smaller wire in the 19 strand will be more likely to be damaged, and I agree with that logic. Best not to drag your lines around on hard surfaces, anyway.

Steve