Mutating Triggers

Use an "after" trigger - If you must use a trigger, it's best to avoid the mutating table error by using an "after" trigger, to avoid the currency issues associated with a mutating table.  For example, using a trigger ":after update on xxx", the original update has completed and the table will not be mutating.
 

Re-work the trigger syntax - Dr. Hall has some great notes on mutating table errors, and offers other ways to avoid mutating tables with a combination of row-level and statement-level triggers.
 

Use autonomous transactions - You can avoid the mutating table error by marking your trigger as an autonomous transaction, making it independent from the table that calls the procedure.