I am already a grad student, but sadly I still have problems with careless computations. In my most recent mid-term (multivariable analysis), I lost 21 points out of 100 because of calculation errors and other cringe-worthy mistakes. If you ask me to explain proofs, I don't believe there will be a problem, but I have no "feels" for computing results. A lot of times, when I have an error, I just don't see it.
I admit too that sometimes I detest calculations and just want to get over with them. Unlike learning a proof, there is no understanding in calculating a result. I still remember learning Taylor series in Calculus -- hated it. After tons of calculations, I had no idea if I was right or wrong, did not know how to check it, nor understand why I was doing a series expansion in the first place. (I got every question in my homework wrong because I could not keep count on the index. The grader gave me 1 point for turning in something ....)
Anyway, there is no use whining; a wrong answer is a wrong answer. Also, I cannot afford to lose 20 points on each exam. What self-check mechanism do other MSE users have?