I have a code green: are the fit indices that Mx produces reliable?
Yes, code green really does mean 'it is probably okay'. This is the least serious warning about optimization problems. However, if the results seem inconsistent with the results of fitting a saturated model, or with a similar model, you would probably want to try some alternative starting values that are closer to these other solutions. Sometimes a Fix All command near the end of the script can be used to see what the starting values are like.