The way the reflexive parroting of 'Gee Willikers situps bad!' has sprung up recently all over the place has left me suspicious. So I dug up the original journal paper.
McGill, S.M. (1995). The mechanics of torso flexion.
Clin. Biomech., 10(4): 184-192.
RELEVANCE: The safety of situps as both a therapeutic modality and training exercise has been questioned for years but evaluation has suffered from a lack of knowledge of tissue loading. The load predictions in this study suggest that performing situps (both dynamic and quasi-static) imposes high levels of compressive loading (> 3000 N) on the low back. The issue of using straight legs or bent knees is probably not as important as the issue of whether or not to prescribe situps at all.
However, this article from 1995 has only 1 citation in another paper. It appears to be just models and predictions of loading without conclusive testing in real environments. I don't doubt this man's credentials, but I am uncertain of the quality of this report that popular body fitness has fixated upon. More research is needed.
In my personal experience (sample size = 1), crunches are more effective at building basic muscle tone than situps. If you anchor your feet you should be able to do weighted crunches as well.
I've had a lot of people recommend Pushups or Side Planks to build muscle tone in my core lately. YMMV.