Commonly used by those who are either too lazy to add the fourth letter, or teen homeboys and teenybopper girls who think that it 'iz totali awzum to speel inkorectly'. These people commonly listen to bastardised punk and 'NU Metal'
The same principle applies, except the 'ass' is replaced by whatever object is source of the impression. Plural version can also be used ("dem ...", see Example 3).
Can also be used in a sarcastic way with respect to the above utilization. (See Example 4, 5)
"Hey man, have you seen this awesome dancer?"
"Oh wow, dat skill."
Friends watching Starcraft 2 streams:
When a new movie/video game is released with insane graphics:
"dat CG" or "dat graphics" or "dem graphics" (plural version)
Dota2/LoL context, when referring to a hero as being terrible/bad:
"dat <hero name here>"
When watching two snails racing against each other:
Big boobs are being displayed.