"This is a new law so naturally there are certain unclear situations and grey areas that need to be ironed out," Manfred Reinthaler from Vienna police told public radio.
"At the same time there is no legal precedence."
Austria is the latest European country to ban the wearing of the full Islamic veil, known as the burqa or the niqab, in public places. The law came into force on October 1.
Government guidelines set out a number of exceptions including masks and disguises at cultural events, work wear such as medical masks, and scarves in cold weather.
But the shark costume case - a mascot for the McShark computer chain - and officers reportedly stopping a girl cycling in a scarf show that some police remain bewildered.
"Lawmakers did not set out the temperature (when a scarf could be worn)," said interior ministry spokesman Karl-Heinz Grundboeck.
There is no central register so the total number of fines of up to 150 euros (USD 177) levied so far is unclear, Grundboeck added.
Polls suggest that the far-right party will garner around 25 per cent support in elections on Sunday and may become junior coalition partners to Sebastian Kurz's conservatives.
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