Using confidential transactions with plain-text ouputs
Is it possible to create a CT transaction, where the inputs reference UTXOs that are not confidential (just as in Bitcoin now), but creating new outputs that are hiding the value using CT's scheme?


Yes, you include a dummy blinding factor.


  What would the network have to do to check that the sum of commitments in the outputs are the same as the sum of clear-text amounts from the inputs? 


With the dummy blinding factor, it would do exactly the same a normal CT tx.

The answer was a lot simpler than you thought.