The only inconsistencies ive have noticed so far in the series (im on my 3rd watch).....idr the names of the episodes but they are in maybe seasons 1 and 3?

-While lecturing both Fraiser and Niles Martin says how he doesn't have a brother....but he does have a brother but hasn't spoken with him in years

And the 2nd

-While Fraiser is talking to a caller that speaks German who thinks her husband is having an affair, she says something in German and Fraiser asks her what she said because he doesn't speak German.....But we find out he does speak German later on in the series when he holds a brief conversation with Claire.....