If you're using the mixer in analogue mode or hybrid audio mode then you should have no problems using the pre-mix monitor as normal. However, the problem arises if you are using the mixer in total midi mode (when nearly all the lights on the mixer are green) and want to use all 4 ASIO channels in your chosen DJ application or DAW app, under these circumstances when all the ASIO channels are required for post mix/main room output its not possible to pre-mix monitor.

Just so there is no mix up, "pre-mix monitoring" is when you want to listen to what the mix sounds like in your headphones first before it goes out to the main room mix. The main room mix or "main mix" is what the room hears. There's a reason I didn't call it "cue" and refered to it as "pre-mix monitoring". To "cue" a track actually means to set it up for play, which means lining up the beat that you want to start on and setting it up so it will mix in how you want it to. Other wise known as the "cue point" or more simply the start point. Notice that CDJ's have a "cue" button. Pressing the cue button doesn't allow you to listen to the track in your headphones, it only helps you set a start point on the next track that you want to mix in as well as return you to it once set. Doing this is called "cueing". 

On the zero 4 the pre-mix monitor buttons are labeled "cue" too. However I guess this comes from the fact that "pre-mix monitoring" can also be refered to as the "cue mix". I guess it should really have been labelled "pre-mix monitor" or "pre-mix" or even "cue mix". Anyway back to the point...

From what I've read even on vastly more expensive alternate pro options like the Allen&Heath Xone3D and 4D,if you want to assign all the availible ASIO channels to correspond to the same number of physical MIDI controller lanes on the mixer whilst in total midi mode (as many people seemingly want to do on the Zeor4) they also lose the ability to pre-mix monitor. It's not just the Zero4. 

Possible work around (depends on the load on your system, the OS you're using and the hardware capability of your laptop)

Simply put, if you really must have this when using total midi mode :

use your headphone jack on your laptop or more ideally a seperate good quality low latency USB audio card for pre-mix monitoring. It this stage it should only be considered for testing purposes unless that is you can get it to a usable and reliable standard of operation.

Ok, you might now be asking how exactly do I do this???!?! Well due to the technicalities of this and the potential results that could be achieved based on the hardware you have I'll do this in two parts. One for using the laptops built in audio card for pre-mix monitoring and one for a seperate USB audio card thats more specifically designed for lower latencies with higher audio output and more defined detail at higher volumes. 

You first need this
Whichever you chose to do you're going to need a little utility called ASIO4ALL which you can get to by clicking this link. Its free to download and use. It will allow to use multiple audio devices at the same time for ASIO streaming.

Using the laptops internal audio card for pre-mix monitoring

I'll say it now and get it out of the way. For most people the results are going to be pretty awful. It all depends on the soundcard that you have in your machine even if you're using a MAC with bootcamp. But like I said the results will barely be usuable and thats even after a boatload of tweaking. Here's why...

Latency issues

When using XP the results were a little better for latency times (only by slights). When using windows 7 it results in a huge latency difference, and even tweaking the settings in order to sync the monitor output to the sound on your mixer usually results in massively huge delays in midi control to software control response when using the Zeor4.  
Trying to set lower latency thesholds for faster response times on most internal laptop audio cards to match the same kinds of speeds on your external pro device will most likely result in a shed load of unwanted audio drops, pops and crackle. Most internal laptop soundcards just aren't fast enough. period, which is strange really considering it is in fact built directly into the main system board with no cables to traverse but thats just the way it is.

The operating system you use will also affect this. XP will allow you to go a little faster then 7. Having said that though based on other tests Windows 8 might actually allow you to set it to a much faster speed with better stable results, but thats yet to be confirmed with actual testing from my side.

But under XP and Windows 7 the best way to go about this is to first find the fastest stable ASIO latency timings that your internal laptop soundcard can handle under those particular operating systems when using ASIO4ALL. You'll also notice that once you've done this the sound being produced from your external pro device gets plays ahead by a couple seconds (if not a few seconds) before the sound thats coming from your internal laptop card. This is because the ASIO streaming rate is much faster on your exteral pro audio device and whilst in this state they're just way out of sync and generally makes pre-mix monitoring near impossible. So you now need to sync them.

To sync them you need to set the ASIO timings for your external pro soundcard accordingly which involves setting the external pro audio devices to a much slower speed in gradual steps until the sound matches what is being produced from the built in laptop soundcard. Under XP and windows 7 you'll find that this causes your external pro device to be so slow that midi controlls, LED VU level readouts and sound in general will be much slower then what your DJ or DAW app is showing/rendering on screen.

Sound issues (which kind of defeats the whole object to begin with)

Then when it comes to finally monitoring the sound, listening to one channel at a time is generally fine but the output and maximum default sound output is very low, nothing that you could actually use in a real club situation for headphone monitoring. If you're using something like ableton you could always assign a serpate audio lane for pre-mix monitoring and add additional gain modules for higher output, but beyond a certain threshold the sound distorts and overloads the output channel. Again if you're using Ableton you can get around this by adding an additional 3 channel EQ module to your dedicated pre-mix monitor audio lane (or even a HQ 8 EQ module if you have the processing power) to then make the appropriate setting to trim down the sound to reduce the distortion at the much higher monitor output levels. However there's a slight problem with this also, it changes the sound dynamic so much that it no longer becomes an accurate audio representation of what you were trying to monitor in the first place. So whilst the sound is seemingly fine in you headphone monitors the mainroom mix might be overloading with too much low end and bottom-mid. Keep in mind this is only when listening to one track in the pre-mix. You need to tweak the EQ settings even further to avoid overload for multiple channels which miss-represents the sound even further within the pre-mix. This is why I generally wouldn't recommend this method of using the latops internal sound other then for testing purposes. But if you can actually get it to a workably usable standard based on the hardware in your machine I'd say lucky you.

Using a separate external USB or firewire device specifically designed for pro audio use

Its basically the same procedure as outlined for the internal audio card but you will in fact get much better results. Again it all depends on the card you use and its capabilities against the load that your machine can handle. Monitoring output will most certainly be much better with less fuss required to get it to a usable standard.

As mentioned before, I've not actually tested it yet on Windows 8, but based on how Windows 8 has performed in other test it might actually help in making this solution even better on the performance front.