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
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.