MediaWiki has its own markup, they call it wiki markup. This is the first lightweight markup I had experience with (if you do not consider PHPBB markup to be lightweight).

Why I don't like it

Syntax for bold and italic. ''italic'' and '''bold'''. This is classic! This syntax comes from very first wikis. But it's bad:
- Easy to confuse '' and " when editing in proportional font. This alone is enough.
- Six characters in total for one of the most used emphases (bold) is kinda uh.
- Not available on the standard Russian keyboard layout.
Headings have to be closed at the end:
```
== heading ==
```
And they also haven't resolved the level 1 problem.
Indentation-based preformatted text.
Inclusion of HTML tags such as <br> and pseudo-HTML tags such as <nowiki>.
Support of inline styling. Sure, because of that there are Mediawiki wikis with really good visuals, but you know the problems.
Ridiculous linking of namespaces File and Category.

Two different syntaces for local links and external links:

[https://example.org text after space]
[[article | text after bar]]

List items are limited to one paragraph.
The syntax for image insertion is the same as linking a text page, except it's different.
Tables that are so strong they replace everything not supported by the markup.
Magic words like NOTOC and #REDIRECT.
Wrong line-break logic.

And for some reason, on mature MediaWiki wikis, almost every page is filled with countless {{}}s.

Why I like it

Still much better than Markdown.

Bracketed links.
Character-repetition-based list nesting.
= for headings.
Tables are useful.
The colon element is cute.
Good macros (called templates).