Is there a distinct advantage that a PS2 port has over a serial/USB port?

Yes! Some operating systems just won't work with USB keyboards or mice. Furthermore some operating systems may not have right USB drivers available during installation which could cause problems with OS installation. Sure, such problems are rare now (but could resurface due to USB 3), but for device manufacturers it pays to have compatibility with older standards.

Now on the hardware side the benefits of PS/2 are clear. The required drivers are much simpler to work with and can be loaded at much earlier stage than USB drivers so PS/2 can be helpful when restoring damaged operating systems which "hang" during certain part of boot process. Another point is that PS/2 KVM switches are easier to design and cheaper to manufacture. Finally the main point is that PS/2 connector itself is relatively small, not very difficult to use and it is sufficient for keyboard and mouse use. As far as response times are concerned, this answer claims that PS/2 actually has an advantage over USB devices.

Another "benefit" for PS/2 is that it is deeply entrenched, old and proven standard and therefore has support of manufacturer "inertia". As we can see when analyzing computer history, it took some time for USB to replace existing serial and parallel ports as well as certain proprietary connectors even in situations where it had significant speed and usability advantage. In current situation from what I can see, USB doesn't have that many advantages when used to connect mice and keyboards to desktop computers where the only major disadvantages of PS/2 are that the connector isn't as easy to plug in as USB and official hot-plugging support which has been mostly back-ported into current systems which use PS/2.

From what I read on this page so far it seems a lot of people are misinformed. The following is information on KEYBOARDS ONLY. I have no idea about PS/2 for mice. The info is from http://www.overclock.net/t/491752/mechanical-keyboard-guide#post_6009418:

Key Blocking & Ghosting

Ghosting is when you press two keys on the keyboard, and a 3rd key - which you didn't press - gets sent to the PC as well. This is very rarely seen on even the cheapest modern boards, because manufacturers have the habit of limiting the rollover so that ghost keys are always blocked.

Key Blocking is as simple as it sounds; you experiencing it when you reach your maximum key roll over. So if you press 2 keys, and the third key is blocked on your board; then you just experienced blocking because your keyboard is only 2KRO.

Key Rollover (#KRO & NKRO)

NKRO is when you can press as many keys as you want at the same time, and all of them go through. This is similar to what some 'gaming keyboards' incorrectly market as "anti-ghosting", even though Logitech and Razer only apply it to the WASD cluster. Note that right now only PS/2 keyboards can exhibit full n-key rollover; though Microsoft and Ducky are just two companies who have already looked at designing NKRO over USB.

xKRO, where x = Any Number, is the key roll over of your board; and stands for the maximum number of keys you can press without experiencing any key blocking.

Many USB mechanical Keyboards are labeled as 6KRO, meaning any 6 keys can be pressed at once without the user experiencing blocking. This is generally enough for most users. Though a limited number of games may have a problem with 6KRO. USB keyboards with 6KRO also allow for a maximum of 4 modifier keys to be used with those 6 normal keys. These modifiers include CTRL, ALT, Shift, & Super (Windows, Command, or Meta Key.) Sometimes this also includes the FN key present on select keyboards.

Key Bouncing

All types of key switches - including rubber domes - do this. When you press a key, the switch "bounces" on and off very quickly as it sets into place. This causes keys to register multiple times for each press. Because of this, keyboards need to implement some sort of debouncing delay - so that once you press a key, the controller waits a certain amount of time before registering a keypress. As an example, Cherry MX switches need 5ms of debouncing time, while rubber domes need longer (exactly how long depends on their quality).

Polling Rates and Response Times

While it is very useful for mice, it's just about meaningless for keyboards. Let's assume for a minute that all switches have the 5ms debouncing time of Cherry MX switches (which is being very generous). Even if you had super human speed and reflexes, every single key would be delayed by at least that much. So really, any polling rate over 200Hz (at best) is absolutely useless, and nothing but market hype. It may even be a bit detrimental, because you'd be wasting CPU time polling the keyboard unneededly. And unlike USB keyboards, PS/2 boards aren't polled at all. They simply send the signal to the PC whenever they are ready to, which causes a hardware interrupt, forcing the CPU to register that keystroke.

PS/2 or USB?

PS/2 wins on three fronts: First, it supports full n-key rollover. Second, PS/2 keyboards aren't polled, but are completely interrupt based. And third, it is impossible for it to be delayed by the USB bus being used by other devices. There are two types of USB transfer modes - the interrupt transfer mode (USB polls keyboard, when key is sensed the USB controller sends the interrupt to the CPU), and the isochronous transfer mode, which reserves a certain amount of bandwidth for the keyboard with a guaranteed latency on the bus. Unfortunately, there are absolutely no keyboards made that use the latter, because special controllers would have to be used, thus making it cost prohibitive.

So if your keyboard supports both PS/2 and USB, and your PC has a PS/2 port, there's no reason not to use it.

In terms of Mice: PS/2 is also interrupt based, meaning that the signal will not have to wait for its turn. In most cases, the time lost is so low that you wont notice it.

However, at least in the game "Starcraft: Broodwar", where your speed can often surpass 10 actions per second in short bursts at competitive level, it is important to have both the keyboard and the mouse on interrupt based actions, other way they overlap in incorrect orders.

I found this to be a problem only at competitive level, but it is still a reason why I give an edge to any PS/2 supporting hardware (Motherboards need 2 PS/2 for me when buying a new PC).

I know that the polling rate is much lower for PS/2, but it does not matter for PS/2 at ALL since the signal will interrupt, not wait for confirmation.

The inconveniences of PS/2 (such as booting and possible damage to the motherboard) are 100% true, but for me at least, since I dont plan to EVER unplug those until they break, there is no downside to it.

In other words, It depends on the buyer and his expectations.

Unfortunately for me, PS/2 mices are a rarity now days and when I do find one I can use, I tend to buy multiple at the same time, just to have spares.