Massless Limit of Massive Field Theory: Right or Wrong?

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If I take the massless limit of a massive field theory (e.g. considering cross-sections or other observables), do I always obtain the "right" massless theory?
 
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It depends what you mean exactly as well as the context. In general, great care must be taken when you take this limit as there are a number of ambiguities that can and will arise.

In some cases, the answer is most likely no!
 

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