It would also be great to have this capability on the iPhone app.

Scott, I'm assuming that you're already planning a route and want to add a marker without interfering with the start & end points in which case a simple workaround is to open a second tab with the CT map, use the address/coordinates to find the location on the map, then add the marker. It should then show up on the other tab without upsetting your route. (Probably best to save the route and hit refresh). 

Alternatively, add the markers before starting to plan the route :-)

If you're not aware, we can generally add an address or latitude & longitude co-ordinates in the 'To' or 'From' boxes. Depending on your location, the address may not be 100% accurate (not all numbers on a street, for example) and there are a variety of sites to easily convert various GPS coordinates into lat/long formats. 

To add, there is also the possibility of adding a viapoint from the 'Route Tools' on the map page (website)

Next to 'Click map to add more points' is the 'Add at...' This will open a dialogue box where you can add coordinates or an address. 

I see also that you seem to be US based? In my experience (a few years ago now) CT sometimes struggled to find exact addresses, especially on long, rural roads. 

Thanks so much for your response. Is there a way I can read in a files with the GPS markers in it?

Sorry Scott, I have no idea what you are asking. 

There isn’t currently a way to import waypoints from a GPX file, sorry, no.