I believe that any such problems are due to non-totality and/or non-strict semantics, and generally aren't important in practice. For example, from the abstract for "Fast and Loose Reasoning is Morally Correct" (http://www.cs.ox.ac.uk/jeremy.gibbons/publications/fast+loos...):
Two languages are defined, one total and one partial, with identical
syntax. The semantics of the partial language includes partial and infinite
values, and all types are lifted, including the function spaces. A partial
equivalence relation (PER) is then defined, the domain of which is the total
subset of the partial language. For types not containing function spaces the
PER relates equal values, and functions are related if they map related values
to related values. It is proved that if two closed terms have the same
semantics in the total language, then they have related semantics in the
partial language. It is also shown that the PER gives rise to a bicartesian
closed category which can be used to reason about values in the domain of the
relation.