If prospects have already gone through a campaign flow, and we change one of the 'Email' actions to use a different Email Template, will this cause problems for the campaign?

No -- changing the Email Template in an Email action after the Campaign has already been running would not cause problems for the Campaign.  

Prospects always move from left to right in a campaign flow -- they cannot move backward and they cannot repeat an action for which they have already been evaluated.  As a result, if your team has been running a particular DemandCenter Campaign for a period of time, and you later decide to change one of the 'Email' actions to use a different Email Template, prospects who have already passed through that Email action will not be affected, but, going forward, prospects entering that Email action will be sent the updated Email Template.

The statistics for the updated Email action would retain the data from the previous Email Template, and would continue to increment as prospects are sent the new Email Template.

To learn how to create a Campaign, click here.

To learn about Campaign Email Actions, click here.