General:
* Filthy: Extremely dirty
* Soiled: Covered in dirt or stains
* Grimy: Covered in dirt and grime
* Unclean: Not clean or hygienic
* Squalid: Extremely dirty and unpleasant
* Grungy: Dirty and neglected
Specific to type of dirt:
* Dusty: Covered in dust
* Muddy: Covered in mud
* Greasy: Covered in grease
* Smeary: Covered in a sticky substance
* Sticky: Covered in a sticky substance
* Oozy: Covered in a slimy substance
Other:
* Unsanitary: Not clean enough to be safe for health
* Unhygienic: Not clean enough to be safe for health
* Polluted: Contaminated with harmful substances
* Tainted: Contaminated or spoiled
The best choice will depend on the specific situation and the level of intensity you want to convey.