Confirming the presence of 4-bromoacetanilide during bromination of acetanilide
I advise against fishing in the mixture in this case. Try to isolate the product, purify it and determine its properties.

Have a look at the melting points of the starting material and the possible monobromination products:


acetanilide 114 °C
2-bromoacetanilide 96.5–100.5 °C
3-bromoacetanilide 81–85 °C
4-bromoacetanilide 165–169 °C


This promising! You can of course use further spectroscopical methods (NMR), but I'd start with the melting point.

You mentioned possible complications for the workup, but I disagree.

The reaction is typically performed in glacial acetic acid with a slight excess of bromine to make sure that there's (almost) no starting material left.

For workup, you pour the whole mixture into a beaker with water that has been placed in a bowl with ice. If you want/need to destroy an excess of bromine, add some bisulfite solution until the aqueous phase is colourless.

There should be some crystals. Filter them off, and recrystallize the material from ethanol.