When I encounter hashtags, I am reminded that language is
alive and a major element of culture. #duh
Hashtags are a word (or string of words) prefaced with the symbol
“#”. First used to label groups and topics in discussion sites, then adopted by
social networking sites like Twitter and Instagram (and Facebook, YouTube,
Tumblr, etc.), hashtags serve as a code or mark for a post.
The purpose is to be able to search or sort posts based on a
hashtag so that one can find posts related to what one is interested in, like. #CulturalCapital
Hashtag is both a noun and a verb. You add hashtags to a
post (noun) and in the act of doing that you hashtag a post (verb).
There is an #etiquette to using hashtags – they should be short,
descriptive, and capitalized if using more than one word. They should not be
overloaded into a post and not redefined from others who used them first if you
intend a different meaning. #SocialNorms
One can search within a site for posts marked with the
hashtag of choice – and there are websites that explain them and show their
usage across the different platforms. #Acculturation
http://www.hashtags.org/
for Twitter
http://web.stagram.com/hot/
for Instagram
A variation on hashtags are identifiers using the “@” sign
preceding someone’s user id. Thus you can not only hashtag or mark a post for a
topic or concept but you can also code it for specific people so that they
notice what you said. #SocialNetwork
Increasingly, hashtags are used for promotion – or
advertising. This is not surprising considering how successful or popular
cultural innovations are often then used by other entities for profit making
enterprises. #Capitalism #Cooptation
When encountering hashtags, it can be intimidating if one
doesn’t know the process, purpose, and format of using them. It takes some
effort to learn about them and some people may opt to just ignore this
relatively new way to communicate. #CultureShock
I hadn’t paid full attention to them until recently when
someone I know started speaking, texting, and emailing using hashtags. They
became so ingrained in how this person thinks that they use them outside the
usual places. #Socialization
However, a texted or emailed hashtag isn’t really useful
since there is no way (yet) to group and view them across the web. (One could
search for them in one’s own email but that is a very limited function.) #Fail
Along with emoticons and abbreviations
that came from “pager speak”, lol, these innovations to our language add
another layer to how people communicate – and miscommunicate. Effective human
communication, particularly across generations and the digital divide, become
difficult when these variations are first introduced and are popular within
certain segments of a population. #Stratification #CulturalLag
On the other hand, they enable communication across cultures
via the web when people who may speak very different dialects and languages can
share information via these methods. This, in turn, can enable people to relate
to one another across very wide cultural chasms. #CulturalRelativism

There’s one more dimension to hashtags and their usage, imo – that’s developed as they’re also used in extension of the previous message expressed, as hashtags have spread across platforms and the acculturation has progressed.
So it’s not only for categorizing, or letting the reader know, which topic you’re in but to express a sentiment (like you did with #duh) or to express humor by adding a word/few words/many words instead of phrasing a wholesome sentence.
Or as you used the #fail-tag to, very briefly, indicate a(n) attitude/judgement of something presented. So that the hashtag itself becomes an expression and a language, not just a description/summary of a topic discussed.