Though of course more language-specific information is needed, general criteria do exist. The finiteness of a clause is basically how non-nominalised it is (Givón, 2001), and, as is well known, the 'nouniness' of a constituent is gradient rather than absolute (Ross, 1973). Thus, the finiteness of the clause can be described as how few NP-like features it has.
Givón (2001) lists the following criteria. Clauses which satisfy a lot of these are less finite (closer to the prototypical NP), whereas clauses satisfying most of these are the most finite:
a. The verb becomes a head noun
b. The verb takes nominalising morphology
c. Tense-aspect-mood distinctions are lost
d. Pronominal agreement is lost
e. Either the subject or the object acquires nominative case
f. Determiners are added
g. Adverbs become adjectives
Sources:
Givón, T. (2001). Syntax: an introduction (Vol. 2). John Benjamins Publishing.
Ross, John R. (1973), 'Nouniness', in O. Fujimura (ed.), Three Dimensions of Linguistic Theory (Tokyo: TEC Company, Ltd.), 137-258.