The inventory scan should scan for all software, but depending on how the agent is configured, there could be a delay. On the client, do an inventory scan and check again, also in the inventory data, scroll down on the right side and look for "Last Software Scan" and see what the date and time are.
There is a bug in Sp1 where 32 bit applications were not showing up... you should look into getting this patchLD95-SP1-CP_BASE-2013-0813
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MrSpike is right about that patch, you would want to make sure that you have it. He is also right about the delay.
Another thing to try is to run the application on the client before running an inventory scan. That will often cause it to be picked up sooner.