What are the causes and solutions for mutating table errors?
The most likely cause of a mutating table error is the misuse of triggers. Here is a typical example:


you insert a row in table A
a trigger on table A (for each row) executes a query on table A, for example to compute a summary column
Oracle throws an ORA-04091: table A is mutating, trigger/function may not see it


This is an expected and normal behaviour, Oracle wants to protect you from yourself since Oracle guarantees:


(i) that each statement is atomic (i.e will either fail or succeed completely)
(ii) that each statement sees a consistent view of the data


Most likely when you write this kind of trigger you would expect the query (2) to see the row inserted on (1). This would be in contradiction with both points above since the update is not finished yet (there could be more rows to be inserted). 

Oracle could return the result consistent with a point in time just before the beginning of the statement but from most of the examples I have seen that try to implement this logic, people see a multi-row statement as a serie of successive steps and expect the statement [2] to see the changes made by the previous steps. Oracle can not return the expected result and therefore throws the error.

For further reading: "mutating table" on Ask Tom.

If as I suspect the cause of the mutating table error is a trigger, one way to avoid the error is to move the logic out of the trigger into procedures.