Actually some form of UNIX has been the dominant OS for quite a while. Taking into account the WWW, 99.9999% of webservers up until tthe latter part of the 90's ran on some form of UNIX box (Sun Solaris Box, OpenBSD, etc...). All the DNS servers at the top level still pretty much run on some form of UNIX box. Before they became pretty much appliances, most firewalls ran on some form of UNIX PC. And aside from financial institutions holding onto the old iron of AS/400's, IBM and HP Mainframes, etc.... a lot of business servers ran some form of UNIX up until the early-mid 2000's. Windows has yet to crack the high-end (i.e. e-bay/paypal runs their database servers off of a huge farm of Sun Microsystems E10K's IIRC...they're not Windows servers).
That said, I'm assuming you're talking about the home consumer market. A couple things could start a definitive POD in say 1989 or 1990:
(1) Apple releases it's grip on it's OS software in the 90's so as to allow for clones and running MacOS on Intel boxes.
(2) Microsoft slammed for antitrust violations for their dealings with computer manufacturers and retail outlets for pre-loading systems ONLY with some form of Windows. US Government allows for retailers to choose which OS's to offer for the platform (OS/2, Windows, DOS, OpenBSD, etc...)
The result of this is Microsoft would not have as much of a monopoly on things (or they might, depends on how they play things). Windows would nevertheless be vastly different as the company wouldn't be directing their product to fly in the face of established standards (e.g. for networking they tried to push their NETBEUI protocol rather than the de facto standard of TCP/IP. Cisco as it came up in usage in IT and grew as a company basically pwn'ed them and Microsoft ended up having NETBEUI to TCP/IP translation until I think either Windows NT or 2000). Windows Server products would probably end up being just a front-end for a flavour of BSD or SysV Unix. And desktop OS's will probably be a lot more like the Linux derivative products we see now such as Ubuntu which are more end-user friendly than the Linux of old.
As far as the home users, pretty much the same outcome as now but with no artificial monopoly by Microsoft. Probably a lot less crashes due to better OS level coding and better communications with hardware developers (rather than Microsoft's current practice of essentially dictating which direction they're going).
As far as viruses, worms, etc... those will still be around unfortunately. With home users, they're not going to get down to whatever is going on with the guts of the OS when they launch applications. Viruses generally weren't written for UNIX boxes as the admins would see the process right away via monitoring their process tables. With Windows the visibility isn't their mainly due to the user; most users frankly are relatively technical idiots as far as this is concerned (i.e. they just want to play games on their PC or surf the internet or email their grandkids or type up a term paper). Viruses only become successful if you don't see what's going on which in the case of Windows currently, you really don't unless you run some third-party tool or Microsoft add-on. This was the same with MacOS as well (remember the nVir virus that would pop up on the resource fork of all of the files? You could manually remove it with something like RedEdit). Viruses remember are an exploit on the unsuspecting masses using OS's that hide the guts of their operations from users that don't see and don't want to see their inner workings. They'll be around but just having a different set of code.
As far as the Y2K bug, this was mainly due to programming (2 digit instead of 4 digit years) on 'old iron', mainly NON-WINDOWS, NON-UNIX machines. So I don't see it deferred or having any issues.