I recommend Eugene Volokh on split infinitives. In short: there's nothing grammatically wrong with them, they've been a part of standard English since long before the language police decided they were evil, and the decision to call them ungrammatical stems from a desire to pretend English is Latin. If you decide to, following my advice, click on the link, you'll also discover that some split infinitives are just so ridiculously awkward as to not be worth using, and some are impossible to avoid without losing some key component of what you want to say.
The first split infinitive in the last sentence is a good example of the former. The second isn't really a good example of the latter, since the splitting could easily have been avoided, but I needed to say what I wanted to say rather than what would have made a good example, and it's too late to spend more time thinking about if I could do it right and say what I wanted. For good examples of obligatorily infinitives from two different linguists, see the Language Log posts here, here, and here.
For the record, I try to avoid split infinitives whenever possible in my own writing, just because I know some people will perceive them as a sign of unintelligence. But there's nothing ungrammatical about them, and it's probably inaccurate even to call them infinitives given that they don't have a form that operates similarly to standard infinitival forms in other languages but do have this splitting function.