Practise can help but looking at what specifically you find hard could also benefit. Eg I found vector problems easy and things with lots of algebra not so easy so I knew what to work on more.
For stupid mistakes:
- In test/SAC situations, how much do they come up there? Generally you'll be more switched on then than when doing private study

- Double check your working at the end
- Check to see if your answer is reasonable right after you have done it
- Don't do too much working in your head when getting the right answer matters (eg exam situation)
I make them all the time still. In methods exam 1 I wrote d/dx (6x^3 + 18x) = 12x^2 + 18, and I can't remember what I did in spec exam 1 but it was something to do with squaring something wrong. Only 2 weeks ago I concluded if a right angled triangle has short sides of 4cm and 6cm, the long side (hypotenuse?) will be 8cm (somehow I got full marks on those questions still...)