Reseeded tomatoes can potentially be a very good thing. In my experience, they are quite drought-tolerant compared to transplants. They are also stronger, and don't require hardening off. There are really only a few problems with this scenario that come to mind:
- The parent plant might have been a hybrid. So, you might get a different kind of tomato than you had before. This isn't necessarily a bad thing (although some people will try to convince you it definitely is). While F2 hybrids aren't always as desirable as the parent, in my experience, sometimes they're more desirable. I've had both more and less desirable tomatoes come from Husky Cherry Red F1 in the F2 generation. F1 is the first-generation hybrid (if you planted a hybrid, that's what it would have been last year). F2 is what it would be this year. F3 is what it would be next year. And so on.
- The tomato may have been cross-pollinated by other tomatoes. Although this isn't terribly likely, it happens. In this case, you'll get a brand new F1 hybrid that you may or may not like. It will probably be at least as productive as the most productive parent, however (given the same conditions and amount of time to grow).
- Reseeded tomatoes are usually in soil where tomatoes had been the year before. This means there may be less nutrients that tomatoes like in the soil. This can result in smaller tomatoes. Adding extra potassium and other nutrients may help them to get larger, if they used a lot the year before. You could transplant them elsewhere or amend the soil to help matters here.
- Reseeded tomatoes are usually on ground where tomatoes had been the year before. There may be more diseases and/or pests present in that ground as a result. However, your tomato may or may not be at least slightly more acclimated to the growing conditions than one that has never grown in them before (which growing conditions may or may not include pests and diseases).
- The tomatoes may not be exactly where you want them. You may also have to cull or transplant some of them if there are too many or if they're too close together. You may still want to cage them, too.
- They may be late-season tomatoes. If your growing season isn't very long, they may not have time to get a good harvest (because you didn't start them in a protected environment early when it was too cold for tomatoes). Early tomatoes should be fine reseeded. Midseason tomatoes may or may not be okay. If they germinate early enough for the number of days you have left in your growing season, you shouldn't have a problem. Giving them extra phosphorus might help them mature faster.
Other than that, I'd say, enjoy your tomatoes. Everything else is probably a pro.
Growing from saved seed is definitely a good idea, as it can help your tomatoes to acclimate to the growing conditions. If they're already acclimated, or used to the conditions, you may not notice a benefit, however.
Early, determinate and/or dwarf indeterminate tomatoes are probably the best kinds to let reseed, I'm guessing. You might consider the following varieties if you want to do it on purpose (squirt the seeds where you want them the year before), provided they actually do stay viable over the winter (not all varieties seem to do that readily):
- New Big Dwarf
- Alaska Fancy
- Mountain Princess
- Gold Nugget
I wouldn't let late-season tomatoes reseed unless you're experimenting, or unless you have a long season. I would be leery about mid-season tomatoes, too.
To encourage tomato seeds that have overwintered to germinate, you'll need to water them, if the ground is dry. They'll grow a lot sooner if you do that. Tilling up the soil before you water it may also help. This spring (2016), I had some germinate from soil I put in a bucket and watered in early to mid April or so, here in Idaho (but the remaining ones in the ground took a lot longer to germinate). I should note that we've had a warm spring. Our last frost and/or freeze this year was around April 16th or so (I covered the seedling on that last frost).
If you like the idea of reseeding, you might consider growing tomatillos. They can spread a lot of seeds even with just a few fruits (like weeds). They do great reseeded. Ground cherries and other garden berries may also do well.