Full Idea
The two main objections to the coherence theory of truth are that there is no way to identify the 'specified set' of propositions without contradiction, ...and that some propositions are true which cohere with no set of beliefs.
Gist of Idea
How do you identify the best coherence set; and aren't there truths which don't cohere?
Source
James O. Young (The Coherence Theory of Truth [2013], §3.1/2)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.4
A Reaction
The point of the first is that you need a prior knowledge of truth to say which of two sets is the better one. The second one is thinking of long-lost tiny details from the past, which seem to be true without evidence. A huge set might beat the first one.