I've taught sewing to a lot of people - beginners through to advanced level. One thing I've noticed is that the same amount of unpicking is done at any level... but only beginners feel bad about having to do it.
The more experienced one is with a sewing machine, the more accepting one is of the need to sometimes unpick and re-do. Practise making perfect (and it's not because we practise for the fun of it!)... experienced sewers are FASTER at unpicking.
Here is one trick I've discovered that a lot of people DON'T know....
1. Get a good seam ripper - fine-point and super-sharp. I think I may have mentioned that I'm in love with my Clover Seam Rippers...
2. Unpick any backtacking/backstitching or multiple rows of stitching with care - don't rip through them as shown below. Cut through a few of the individual stitches and pull the threads out.
3. On a straight seam - ONLY IF YOU HAVE A GOOD SEAM RIPPER - you can gently slice through the stitches as shown below. The longer spike on the seam ripper goes to the top and the little ball on the underside. You shouldn't need to use any force to cut the stitches.
BEWARE cheap or blunt seam rippers! If you don't immediately slice through the stitches then DON'T FORCE IT!!! You can slip and slice through your fabric!
So.... what do you do with all the little bits of thread left in the fabric? Pick them out with your fingers...?
4. No... get a lint roller to do the work for you! (Sticky tape will also work, but is slower). I'm a big fan of the $1.95 lint roller from Ikea, or you can buy similar things in most sewing shops and even supermarkets.
Roll it on the right side of fabric...