The first thing you should do is report the error. When viewing the passenger record, there is a box at the very bottom right which says "If you believe there are transcription errors in this data, please send us your suggested corrections." Click on the live link in that box to tell them that the passenger record is linked to the incorrect ship's manifest. If you are lucky (like I was), they will send you instructions for viewing the correct manifest.
Or you can use the stevemorse.org website to try to find it yourself. From the main page, click on Ellis Island, then Ellis Island Manifests, and then follow the instructions to use the tool to find "missing manifests." BTW, the same tool can be found on jewishgen.org.