SQL Server 2012 Table Partitioning - Have I done it correctly?
Unfortunately, you are correct the suspect that the partitioning you created can get you in trouble.

First of all, partition elimination only happens if the partitioning key is in the query you execute. In other words, any query that does NOT contain AcctYear will do (at least) 31 seeks. SQL Server has no way to know which partition to search if you don't specify it.

Second, there are several issue with the optimiser and partitioning that prevents elimination even when it is theoretically possible to achieve it (like in your  example). In SQL Server, you can think of a partition as a hidden index column. In your case, if you were to index in such a way that job number was leading the index, your query with both AcctYear and job number might do only a single seek.

If you add the most common queries you expect to your question, it would be possible to advise you on the best partitioning strategy that achieves your goal.