This is a confusing one, I would agree. Technically, MoiraWendy is correct. If the subject is plural, then it is 'There seem'. If you reword the sentence: 'Three principal factors seem to be involved: ...' then it will make sense, because 'There' is an adverb in the original sentence. However, you will hear: "There seems to be 3 factors involved: ..." all the time. I myself, in speech, will frequently make this 'mistake' as do hordes of other native English speakers!

There seem to be three ... is correct. There SEEMS to be only ONE factor. IT seems to be ... There SEEM to be THREE factors. THEY are all important in.....

"Seem to be" is correct, as thuy Bien explained in her comment. The subject is plural.

I cannot explain the rules, but "There seems to be..." is correct. I'm a native speaker from the USA.

I may need to take some English lessons on Italki :)