I love the 'Add family events' section on the LHS of the Home page. Shame it's so short! It'd be great to click on a 'See more' link to go to a page with all missing info on the tree.
Even better would be to also have on that page all the inconsistent and strange info, e.g. children older than parents, partners with 100 years in age difference, etc.
Part of our windows client application 'Family Tree Builder' includes a tree consistancy checker, where you can get consistancies as you described. You are welcome to export you tree through GEDCOM and import it there, and check your tree for inconsistancies.
Excellent. So you have the functionality already! I'll look forward to seeing it ported to the website, so that I can use the 'fix it' link/button there as well (rather than seeing the errors in the software, and fixing them manually on the website).