No, I don't think you did anything wrong. Some servers are just picky, some sometimes get slowdowns and not all of them are online all the time. Some of them just need to be configured in such a way that they get auto-connected after some retries.
There are some exceptions. Some servers are Japanese-exclusive, others are speed-restricted and other require a minimum of shared material. I'm sure that the only limitation for you would be the Japanese-restricted servers. I can tell you that INC (the second server), Magicant, TRAIN (the second server) and ゼロ戦 work for me without problem even with my connection. You should also be able to connect to High-Point and KOOL too.
If you get a message, first translate it with one of the several online tools and reply in Japanese also. The important part in Utatane is making trading contacts, so try to answer all message that you get. Some messages are automated, be sure to read them as precisely as possible, to avoid confusing real people with automated messages. Mugesz can probably tell you some strategies to get rare files, since I've not managed to get something important. It will help you if the filenames of your shared files are in Japanese (something that I can only do for some of my files). I'm not sure if Utatane is able to read folders with Japanese characters, since I've had some problems with that (it may be something related to my configuration). But files with Japanese characters are no problem with AppLocale.
When you get a message, you will know it. Utatane will blink in the system tray icon. Double-click to open the message. In that Window, everything is, more or less, pretty easy to understand. If you want to send a message, right-click in the file that you want to get and select the option "send message" to show the message Window. The rest depends on your trading and communicating skills, which is not an easy task actually.