I realise this is an ancient post, but it got bumped, and I got curious...
After digging into things a little and thinking about usage here and on other SE sites, I wanted to provide a counter-point to Kevin's existing answer as I dispute the idea that there's a "general trend (network-wide) to use plurals" for tag names.
After looking through the top couple of hundred tags on several SE sites, there does not seem to be a trend towards plurals... Instead, I think Kevin's observation that "people are just as likely to ask questions that apply to multiple [of a given thing] as a single one, so (given that we can only have one) the plural makes more sense" provides a hint as to what is actually happening. From what I see, it appears to be about the most common usage scenario of the given tag that drives its pluralisation.
For example, on Meta.SE, it's true most tags are plurals, but on Meta, usage tends to be about collective concepts (comments or edits in general), rather than specific examples (and in fact they have semi-redundant tags for some things, like specific-question vs questions). Tags covering topics that are more likely to be discussing the singular, on the other hand, maintain singular tags (eg. bug, retag-request, error-message, etc).
Moreover, if you take a more technical site, where questions are naturally more specific (like Stack Overflow itself), tags seem to be much more likely to be in the singular form, because questions tend to be more focused on specific singular examples. Looking at tags in the top 200 where pluralisation even makes sense (many tags aren't even candidates for pluralisation), ~70% are in the singular. This is intuitive, since you'll generally be asking a question about a specific algorithm or database issue than just musing about algorithms and databases in general. Similarly on Super User, you get questions relating to a specific hard-drive or graphics-card, than about those topics in general so SU also has tags primarily in the singular.
I think the same applies on PSE. Most questions on PSE tend to be about – or often, are an example of – a specific instance of the given tag topic. We don't often get questions about riddles generally, we get singular examples of a specific riddle. This is consistent with the de facto standard that seems to have risen on PSE, where most tags are singular barring a limited number of exceptions (such as topics where the plural is the only form that is likely, or outliers like those in your post).
Therefore, I think that the singular form should be the default tag naming policy for PSE, with the exception being cases where the common usage would be plural (eg. I think letters is fine being plural).
I disagree with Kevin and posit that the tag naming trend across the network is towards the most likely usage of that tag — i.e. singular if questions are likely to focus on a single example of the topic and plural if questions are likely to focus on the topic in general.
...and back to the actual question...
Looking at the tags mentioned in this post, as well as a few others from the top 100 or so tags, I think:
I'm not sure what's involved in tag renaming, and ultimately I don't think this is a big enough issue to necessarily warrant undertaking any massive retag effort, but as a point of policy/reference, I think we should be taking the "primary usage based" approach to tag naming as detailed above. That way, at least when a rename opportunity arises, or a new tag is created, we have some general consensus/guidance as to which way things should be moving.