1) Find the issue and locate a suitable fix.
2) Create a PK3 that contains ONLY your fix. Do NOT touch the original PK3 at all. It will be explained below why.
3) Name your patch PK3 something like z-original-filename.pk3. The z- prefix makes sure that your PK3 is loaded last and will override anything from the original PK3. With missing files this is not so important but is still a good habit to have.
4) Include a simple text file that includes details about what has changed or been added. This helps others work out if they even want to use the patch PK3.
Now you can play the map with your fixes and so can other players.
Why not update the original map?
There are a number of reason however the most important is you do not want to create a conflicting PK3. For example, at a LAN game or online a number of security and anti-cheat checks are performed. If you have a PK3 that is different to that of the game server you will not be able to join that match.
Another reason is you are not the author of the original work. It is not your job and you should NOT touch the released version of someone's work. While different, it is a little like going around the neighbourhood and fixing someone's house because you see a problem without asking the owner first.
The next reason is once a modified version of a map is available to others (via a download link for example) you have polluted the Internet with an invalid version of a release. It now becomes harder to work out which is the correct version.
While all this is not a problem at home playing bots, it is an issue with online and LAN matches.
Correctly compiled patches are welcome to be submitted to ..::LvL as well. Use the contact page - http://lvlworld.com/contact - to submit them. I'll add patch files to the bottom of the review for others to download.
Anyway I could try to make some patches myself and submit here because there are some issues I noticed with some maps.