Hiya!
I love Middlemarch, probably my favorite book, if I were the type to make 'ultimate' lists. I found Caleb to be a great example of an INTP, e9 (what I am). My favorite character by far.
I will keep your values and note if mine differs:
Dorothea: INFJ - I would also offer up INFP. She has more mental flexibility, and is less judgemental than I see INFJ as. I can see her as a healer, and the parallel with St. Theresa (I think, an INFP) is interesting.
Lydgate: xNTJ - perhaps an ENTP, instead? He is easily lead into money difficulties, and seems to enjoy the company of others. While he clearly enjoys intellectual pursuits, he does not exactly pursue them with the diligence you would see from a J. He has a brilliant mind, to be sure, but his scientific excursions seem to be merely "dabbling". Also, his enjoyment in reading/thinking about these scientific matters seems very clearly Ti to me.
Bulstrode: ISTJ - yes, exactly.
Caleb: ISTP - I really think INTP. I identified very much with this character. He is, however, a rather gentle version (not, I think, an e5).
Rosamond: ESFP - in contrast, I think Rosamond is a J. She has very decided opinions about how things are, and uses the J-like filter to just "not hear" reality at times. She can be very rigid. I would suggest she is an ESFJ, like her mother.
Casaubon: INTJ - agree
Mr Brooke: ENFJ - disagree. I think ESTP. Mr. Brooke doesn't have the true idealism of an NF, here merely wishes to be popular. He is an eternal dabbler, as you see from his constant referencing of "oh I did a little of that" comments. Almost certainly a P, and not an F - or he would have more feeling towards his neglected tenants. He also has difficulty in public speaking, I find that hard to match to an ENFJ.
Fred: ISFP
Mary: ISFJ - I think you have Fred and Mary correct.
Mr Vincy: ESTJ - yes.
Farebrother: xNFx - Farebrother, recall, does not really feel the calling to be a priest. He could be an INFJ, or INFP, but his intellectual interests to me seem to suggest, possibly, another INTP. However I find this character very balanced. Another e9, for sure.
Will: ENFP
Rigg: INTP
Featherstone: ESTP
Mrs Vincy: ESFJ - yes.
I have a hard time saying on these last few, I haven't read the book extremely recently.