"I was wondering if you have any suggestions for alternatives to the zigzag stitch for these pants. I have an old machine and it only has the straight stitch. Thanks in advance!"
I'm glad you asked! There really is no substitute for sealing your seams with something like a zigzag stitch. As you may know, a zigzag stitch can seal in the seam allowance to make sure that there are no fraying edges on your work. Fraying edges can eventually lead to totally eroded seams.
On old machines that don't have a zigzag stitch, you can try to manipulate the fabric to actually stitch a straight stitch in a zig zag pattern. beyond this, I would really suggest hanging out in front of the television one night (put on a long movie for pants, maybe a couple episodes of Breaking Bad for the seams on a shirt).
Okay, really, hand-stitching a zigzag seam isn't really all that difficult, and doesn't take that much time. But if you are really short on time and without a sewing machine that provides a zigzag seam, you can always try a seam sealer like Liquid Stitch. This product is a kind of thin, wash-resistant glue that will make sure your seams don't unravel.
Taking care of your seams is an extra step that can take a little bit of time and determination. You'll be glad you did though, because your clothes will last a lot longer through wash and wear with 'sealed' seams.