listening with one headphone is only going to be the left signal, which is the Mid signal and Side Left, so you will not be getting a clear picture of the stereo image.
"Phase" is pretty much like bandwidth that you get in frequency ranges, or on notes, you can only have so much so choose your sounds wisely... the most basic example of phase cancellation, just go into a synth with a saw wave and turn it to two voices, and turn the detune up. that flanging/chorus sound you hear is the result of phase cancellation. now turn it up to 6 or 7 voices, and turn the detune up. the part of the sound that is disappearing is because the waveform is moving at a slightly lower or faster rate which effectively cancels itself out. try layering this hyper-lead sound with a crystal clear piano, with no reverb, at the same volume and you will hear how that saw lead is now effecting the clarity of the piano sound. now add a long reverb to the piano, and a long reverb to the saw wave, suddenly nothing is really clear. that is good example of all the problems you will be facing when you try to have two different sounds playing on the same note frequencies in your song. if the sounds have inconsistent dynamics it will get even worse, modulating this effect, and causing even more inconsistent dynamics because now the peak level is jumping up and down.
start working with a plug-in that lets you listen to the signal in mono, some monitor controllers have a mono button that lets you hear in mono, which is like hard mono compared to doing it in the DAW. any mid side plug-in will let you hear the mono signal, just by muting the side signal.
The super quick method of making something more mono compatible, which i'm not sure if it is the best, but it does fix having the drastic reduction in volume when listening in mono is to just get a mid side plugin that lets you adjust the volume of the side signal, and turning down the side signal to 40-50%. trying to preserve the stereo width, while balancing mono compatibility is key.
A few other things that help with stereo image, put a plugin on the master that forces everything below 150-200 (i use 150 by default) to mono. when you are using a lot of mid-range sounds like pads,chords, saws, use a mid-side eq and just be mindful of the stereo image.. sometimes you want to have lows in the sides and sometimes you dont, use the mid-side eq to try and clean it up by removing lows from the side signal. I would say its BEST to have low-mids in the sides if you can do it, but sometimes that might be what is causing the problems. generally most things that do not sound like direct mono are going to cause problems with mono compatibility. having the core elements, bass, chords, melody, still sounding close in mono is all that is needed and if some of the reverbs disappear or width then thats generally okay.
another big tip would be to balance what channels are in stereo and force others into mono. in a normal band recording, the vocals, bass guitars, solo instruments are sometimes recorded in mono, then sent to a reverb which gives it a stereo impression. but in a DAW when using synths, most channels default to stereo so its a good idea to think about which instruments don't need to be in stereo and force them into mono. if you do have huge phasey elements sometimes you need to add stuff in mono (leads) with less information or it will just get lost into the sea of reverb that's in the background of your track.