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Let me preface this by saying that I know my advice (if I can even call it that) won't apply to all nor will my situation mirror all, but I just wanted to share my experience for those who will eventually struggle with the decision to cancel.
I took the June 2014 LSAT, felt I did poorly on a RC that most people felt was easy, and then had two LG and struggled on both. Going in my average was a 171 but the day before the test I had gotten a 166 on a PT. When I left I thought my realistic scenario for a score was a 166-168. By the time I got home I had started to worry about everything though (smudges, skipped questions, and even whether I had done an entire section wrong by accidentally skipping one bubble). I didn't cancel but I've been reading posts from other who mentioned cancelling scores they felt were going to turn out similar to mine.
For the last three nights, I have had nightmares about botching entire sections and bombing the whole test. I had basically resigned myself to accept the low score I thought I knew I was going to get, and to make sure to cancel on my next test if it felt it was going similarly. As you might have guessed, I ended up doing well (actually a personal best at 176). My advice to others thinking about cancelling or struggling with similar anxiety is to not take someone else's analysis of their of their test and (even subconsciously) apply it to your own. The waiting period is bound to make you question yourself, and in some cases a cancellation might make sense. However, I suspect that for a large number of cancellations, fear and anxiety rob someone of what would have been a perfectly acceptable score. Just a positive experience from not cancelling that I thought I'd share.
I wholeheartedly second what CFC152436 said about avoiding slipping into a robotic mode. If you are used to a certain set of games, have practiced primarily on a certain set of games, and then encounter something else when you first take the LSAT, then test day jitters are bound to cause you to have more difficulty solving the game than even what you already might have.
My recommendation for dealing with those games is to make sure to use a lot of the older tests (1-20) in your prep. Many of these have nontraditional game types and practicing taking these games in a PT environment (not an isolated LG practice) will help prepare you on how to encounter completely new game types in the middle of a 4 hour test.