General synonyms:
* Disperse
* Spread
* Distribute
* Diffuse
* Disseminate
* Strewn (past participle of "strew")
* Sprinkle (for small objects)
* Dissipate (for something that fades away)
Synonyms emphasizing randomness:
* Randomize
* Jumble
* Scatterbrained (for thoughts or ideas)
Synonyms emphasizing direction:
* Fling
* Toss
* Throw
* Sling
Synonyms emphasizing a specific action:
* Sow (for seeds)
* Splash (for liquids)
* Sprinkle (for small objects)
* Spray (for liquids)
The best synonym for "scatter" will depend on the specific situation and the nuance you want to convey.