Before I am done recording these actions I like to group them.
Why are you trying to record steps like moving actions to group them and such. You should stop recording the actions. Then move, group and organize them the way you want. After that you should save all the action set you messed with so you don't loose the new actions you recorded and have save them organized and grouped the way you want. If you record steps the move and copy actions mess with actions when you play the action these steps are recorded in the action will more then likely mess up actions and the grouping you did.
Post a screen capture of the action steps of the action your having a problem with. Have you looked at waht is recorded in the action?
I'm sorry I don't believe I worded my processes quite right . I am not grouping my actions at all...rather I am grouping the adjustment layers in the layers panel into one group...this group will then be renamed to whatever I want to call my action. I can play all of my actions just fine however I am having problems playing the ones that have all of the adjustment layers in a group. I hope this helps sorry for any confusion and any suggestions are much appreciated!
Please post a screen capture of the actions palette with the action fully expanded so we can see all the steps and recorded settings. Or save your loaded actions as a text file and extract the problem action in text format and post that here. To save all your loaded actions in text format hold down the Alt|OPT+CTRL|CMD then use the mouse to pop the Action Pallets Fly-out menu and drag down to save actions it will default the file name to Actions.txt.
Witout seeing the action I can not help you.