To be exact about it, start by separating chemical degradation from physical degradation, because they fail differently and they are detected differently. Chemical degradation changes the molecule and shows up as new peaks on a chromatogram. Physical degradation aggregates the molecule and often shows up as nothing at all on reverse-phase HPLC, because the aggregate never makes it onto the column.
Light matters for specific residues rather than in general. Tryptophan and to a lesser extent tyrosine and methionine are photo-labile; a sequence without them is largely indifferent to ambient light over the timescales in question. Amber glass is cheap insurance rather than a requirement.
The underlying point is that freeze-concentration is the mechanism people miss. As ice forms, everything that is not water is excluded into a shrinking unfrozen fraction, so the local concentration of peptide, buffer salts and preservative rises sharply. If the buffer components crystallise at different rates, local pH can shift by more than a unit. That is why a phosphate-buffered solution can behave badly on freezing while an unbuffered one is fine.
Deamidation kinetics for asparagine in peptides are well characterised and strongly sequence-dependent: the residue following the asparagine dominates the rate, with glycine and serine at the n+1 position accelerating it by an order of magnitude relative to bulkier residues. That is why two peptides in the same buffer at the same temperature can have quite different shelf lives.
The caveat is that "within specification" and "unchanged" are different claims. A vial can lose a few per cent of content and still be usable for its purpose while no longer matching its certificate.
If the material arrived warm and it was lyophilised, test it and proceed on the result. If it arrived warm and it was in solution, the result is more likely to be interesting than reassuring.