Luckily the hole in the sweater was along a seam, so entirely fixable. Unfortunately sewing a straight seam is really a challenge for me. And the hole, while on the seam had frayed out a bit, so I worried that trying to fix the hole with a straight seam would make the sweater look puckery. Seeing as the hole was on a front shoulder seam, puckery sewing would be noticeable.
While I cannot stitch a straight seam, I am pretty good at embroidery, do I dug out my handy copy of Mary Thomas's Dictionary of Embroidery Stitches. Mostly I look at this book and never do any stitching, but this time I found a lovely decorative stitch and got to work.
Here's how it turned out:

And here's the detail:
I must say I am pretty proud of myself both in terms of craft and frugality. Now I just need to learn how to darn socks.