The pluses outweigh the minuses...if executed correctly.
As far as BYOD is concerned for the average user, the benefits include choice of device, choice of apps, the freedom to customize the device as their own and the ability to work while away, if they so desire. True this will not apply to all users generally, but most end-users feel like IT's mindset for years has been authoritative at best and absolutely iron-fisted at worse.
This "draconian" mentality on behalf of IT may have been necessary at times and in certain organizations, but IT is dynamic - not static. We have to roll with the punches so to speak and if the current wave (due to a combination of younger end-users entering the work force, more tech savvy employees, economic downturn and cut-backs on non-essential spending, etc) means that corporations cannot (or do not want to) spend $$$ per user on a tablet or smartphone, or both, then this offers up a unique solution to both parties. Enterprise can offset the expenditure by allowing the end-user's to foot the bill for a device they may already own and users can feel empowered to use their personal equipment for work, if they so choose. It also brings with it a certain comfort level that they can work from where ever they are and with the apps they are familiar with - so long as the job gets done.
As far as Enterprise is concerned, they will need to make adjustments to support such traffic on their networks. But most of the time, with the heavy shift to web-based (cloud) apps, this is a non-issue really and secured access to company servers can be implemented using a variety of low-cost, industry-standard solutions, like VPN for encryption, VLANs for network switching and security policies on the devices themselves - even on corporate email/Exchange!
Lastly, as far as support goes, this is a biggie. Being the sole IT support at my location, this one kind of falls between my skillset and my judgement. Personal devices - even if used for work - are taken on a case by case basis, at my sole discretion. There is no policy in place to address this issue, but the company outlook is basically "if it's procured by the company, you support it; if not, you decide how to proceed". With that said, I do my best to support all devices equally. However, there are times/situations where the work load does not allow me to fully-support the personal device(s) or they have been dropped and may need a part replacement that is out of warranty. In these cases, the issue may be resolved through other means, either through out of warranty repair by authorized repair services or other options, as related.
Bottom line, BYOD is not for everyone and even if it works for your company, not all facets may be a perfect fit. But it is a two-part solution and both the company and the end-user need to sign-off on it and make the necessary changes to make it work out as best as possible.