First-rate, second-rate, and third-rate

If you told Prof B that he was second-rate I don't think he'd take any comfort at all from the fact that at least you didn't label him third-rate.

For most purposes, first-rate means "excellent", and both second- and third-rate mean "not good". We actually use second-rate maybe 3-4 times more often than third-rate, but they don't normally both occur in the same utterance unless someone is (somewhat facetiously) saying that something else is even worse than something that was already labelled second-rate.

Historically speaking, third-rate has naval origins - within which context, third-rate ships often actually had the best compromise between sailing ability (speed, handling), firepower, and cost.

But in common parlance no-one thinks like that today - second- and third-rate aren't normally used to indicate different points on the scale of "less than first-rate".

From the Merriam-Webster dictionary:

THIRD-RATE (adjective) Extremely low in quality or value : worse than second-rate. First known use was in 1814.

SECOND-RATE (adjective) Of second or inferior quality or value : mediocre. First known use was in 1669.

FIRST-RATE (adjective) Of the first order of size, importance, or quality. First known use was in 1671.

Taking into account the above definitions, I would say that it is not optimal to use these words in certain situations when doing an explicit comparison. Instead of third-rate you could use a word such as "tertiary," which implies the third position in a series of rankings, as opposed to "third-rate" which has primarily a negative connotation. This won't work for everything, but it's an idea.

[number]-rate, going by dictionary definitions, does not seem to imply ranking outside of a general measurement of good/mediocre/poor quality.

In your second example (regarding Prof. C) I believe calling him third-rate wouldn't necessarily claim that he is the worst professor, but rather a terrible one in general.

I would suggest that you avoid using "second rate" and "third rate". Depending who you're talking to, you could refer to:

Prof A as "first-rate"
Prof B (perhaps) as "average"
Prof C in the terms you give, as "the worst professor you've ever encountered"

"I may not be a first-rate composer, but I am a first-class second-rate composer" --Richard Strauss

I like this example because it gives a bit of specificity to the difference between "class" and "rating."

While I bow to the dictionary definitions in the other answers, I have certainly heard finer gradations than they imply. I have heard third-rate university used in favorable(!) comparison to eighth-rate. (The latter is, I believe, beyond the ordinals of British naval practice.) Google shows a similar example of eighth-rate in a sports magazine.