Hello Gerry905,
Your sentence is not a very current expression, sounds more like a joke "made up" for an occasion.
Please, note that the suffix
-nak/-nek is not used exclusively to mark the Dative, as it is the case here.
Nevertheless, the use of this suffix here is a typical one: it is needed as a part of an expression. (Like e.g. "to" in
look forward to something in English which does not appear in the same meaning as in "I wrote a letter
to him".)
The verb
érezni appears in this construction: "érezni magát valami
nek" (= consider oneself something) so your sentence could be translated as:
Shall I consider myself as* a mistake?
The same construction could also be used in a less figurative sense like in:
betegnek/gyengének/erősnek stb. érzem magam (= I feel ill/weak/strong, etc.)
See also
this thread.
Edit: *
as is probably my mistake in the translation (on second thoughts) It is not needed, is it?