Install SP 3 on SQL Server 2008, where merge replication is running I have a SQL Server 2008 and I should install Service Pack 3 for it.

On my server there are several databases replicated, and mobile devices sync data via merge replication.

Can problems occur, if I install SP3, especially with my mobile devices (where SQL CE 3.5 is running).

I can't update all of the mobile devices.
You should be able to apply the SP3 without dropping any merge replication publications.  The order of upgrade should be to upgrade (1) distributor, then (2) publisher, then (3) subscribers.

The SP3 is for SQL Server 2008, not the SQL CE 3.5 mobile tools.  Since you are running merge replication then I assume that you have SQL CE 3.5 SP2.  So all should be well.

However:  Do you have a test system and test mobile devices?  If so, test your upgrade in the test system first. I always like to deal with suprises in a test system before applying changes to Production.