OK, because I everyone is getting so confused about kernels and Clockworkmod recovery, please read this.
ROM Manager is not built to work with the Mesmerize or the Showcase.
***STOP TRYING TO USE IT AND COMPLAINING THAT IT DOESN'T WORK***
At this point in time there are several kernels that have been built by the guys in the Fascinate forum. All of these kernels have been built from the same source worked up by jt1134. All of these kernels actually work for all three phones. So yes, they will actually work on your Mesmerize/Showcase. To install one of these kernels you need to have a working recovery. This means you don't flash it in Odin, but from your sdcard in recovery.
In this thread is a working modified Clockworkmod recovery that is also built to work with all three phones. To flash it, you would either need a recovery that allows you to flash a zip file, or you can flash the tar file in Odin. If you have a recovery that goes straight to red recovery, you don't necessarily need this. If you have to apply update.zip from blue recovery to get to red recovery, or if you don't have red recovery at all, this is for you.
It does not require ROM Manager to work. All you have to do is boot into recovery, either by adb (reboot recovery) or by three button method (power off, then hold power and volume up/down until you see samsung, then switch to power and volume down).
Once in recovery, use volume keys for up/down, and power for select. If you accidentally hit home, your screen will go black. Just hit home again to turn it back on. To flash something, you will select "install zip from sdcard", then "choose zip from sdcard". Then you will find whatever it is that you want to flash and select it, confirm, and away you go. When done, use the menu key to back out to the main menu, and reboot. If you have multiple things to flash, you can do them all at once, usually with no need to reboot between flashing.
If you have a voodoo kernel installed, and you are going to do a backup, restore, or Odin flash you must disable lagfix before doing so. You can do this in recovery by selecting "voodoo" and then "disable lagfix", or you can use the voodoo control app from the market to disable lagfix.
Note that it is also good practice to disable lagfix when flashing ROMs and mods as well just in case something happens and you need to do a recovery or Odin flash. If this happens, it's not an easy process to recover from.
Hopefully this answers most of the questions that people have.
You will want the TouchWiz kernels NOT the AOSP kernels.
Link to kernels and Clockworkmod recovery
Any questions can be directed to the original post or you can go to the irc chat room in my signature for help.