In this thread, I would like to present several suggestions at once. Perhaps each of them is not too difficult to implement, but the point is that many such suggestions have accumulated. Also, I will add a poll here, since it has become customary in this section.
1. The first suggestions concern search functionality. I propose fixing the search in sections with disabled counters so that it works correctly, instead of how it currently functions:

Sorry, no matches found. Please try different topics.

2. Another problem with search is short words. Yes, I understand why one- and two-letter words are excluded from the search; the number of matches would be simply enormous. But can't the forum handle the load from searching for three-letter words? Moreover, some three-letter combinations are quite rare, while others could simply display something like "Sorry, too many matches," if technically necessary.

3. There is a lack of advanced search by topic rather than by section. It’s a small thing, but annoying. To use advanced search by topic, you have to select the entire subforum containing that topic. And frankly speaking, the functionality of advanced search leaves much to be desired... Can operators even be used in it? Apparently, initially it searches for a match with at least one of the listed keywords – why not all of them together? Or why can't we configure it to search for messages that contain all the specified keywords? If possible, it would be good to describe this in detail, preferably not just in the help section, but directly in the search form itself.
In general, I would briefly describe this point as "increasing the capabilities of advanced search on the forum."

4. Another thing that, in my opinion, deserves modernization is embedded videos. Currently, to embed a video on a page, you have to use old YouTube tags, and manually copy and enter everything because automatic generation of such tags has long been removed from YouTube itself.Example.
It looks like this:

And the modern standard, generally speaking, is something like this (I slightly "messed it up" here; otherwise, even under the HTML tag, the forum censors it mercilessly...):

< iframe width="560" height="315" src="https://www.youtube.com/embed/LMzOHfOSRl0" frameborder="0" allowfullscreen>

But it is perceived by the forum engine as malicious code:

[An attempt to use malicious tags has been detected. Please notify moderators!]

A separate headache is that the old code requires Flash to work, while the new one uses html5.
In general, I suggest adding support for the new code.

5. Now about signatures. I don't know how demanding they are on forum resources, but if there are enough resources, I think it’s time to ease the restrictions on signatures. For starters, make it more obvious – text. How much does a single printed character weigh? A byte? Then why is there a limit of 500 characters in a signature? Yes, I understand that reading huge walls of text in signatures would not be very pleasant, but various tags also count as characters. And isn't 500 characters too little? It's roughly six lines. I believe you could allow even more. My suggestion is to increase the limit to 1000 characters (or so. Something like 800 should also be sufficient, but here the question is, what unnecessary limitations should we add?).

6. Images in signatures. Here, I cannot refer to their tiny weight, but still, if the load from them allows, then the restrictions should also be reduced. This especially applies to the area of images. The following points are particularly strange:

A user's signature cannot contain more than two large images if there are no small images.

Images with an area larger than 500x140 are not allowed.

As a result, to insert a large image (larger than 500x140), you have to cut it into two and insert them this way. Very strange. Why not just set a limit on the total area of images in a signature and make it not too strict? Unless you want to limit the width so that signatures don’t inadvertently "stretch" the image on the screen, as happens with large pictures. So, in conclusion:
-limit the total area of images (something like 500x500 pixels would be more than enough, in my opinion).
-limit the width (I won't say how)
-limit the total number of images (otherwise they will put a million animated emoticons; we know this)
-possibly limit the total weight of images to reduce the load on the forum. Well, if necessary.

That's all. Here I should note that I do not know exactly about the technical possibilities of implementing one or another point. Also, I am not insisting on precisely such changes; perhaps something needs to be reformulated. But I believe that such "innovations" would be useful for the forum.

Extra

7, 8, 9, 10. Drakkosha's suggestions. In particular, about slightly increasing the size of avatars and adding spoilers. Separately about spoilers: Shaman has already managed to implement something like this. And then we discussed it with him and further improved it.

11. Old-school reputation system. Personally, I am more against it if the implementation corresponds to what was described to me (I didn’t experience this myself). But taking the best moments from there, such as the ability to see pluses and minuses for a post, would probably be good.

12. About attachments. It really makes sense to do something similar, that is, add the ability to upload other types of archives. And you could also increase the maximum size of archive attachments.