charset problems

I tried to upgrade my 0.9.6.1 install to 9.6.3., and ended up with charset problems.
It is said that

Revised installer that helps to properly set database charsets and collations while maintaining compatibility with upgrades for existing installations. This should help with non-English multi-byte languages.

but all my local characters got messed up.
When I try to define database, i cannot SET CHARACTER SET, but have to SET NAMES :

The result is wrong interpretation of eastern european characters.
How can I fix this?

I managed to install 0.9.6.3 version for another client who uses different webhost, and the only apparent difference is php version.
The webhost that works has # PHP Version: 5.2.9, while the one on whitch 0.9.6.3 install makes problems with local characters uses # PHP Version: 5.2.8
Could that be the problem?

Sounds like the usual mysql charset problems. My guess is the under 9.6.1 your database connection operated with the wrong charset, this usually does not affect anything until you switch to the right charset as you found out.
Lets try some troubleshooting:
1. What encoding are you trying to use?
2. On your old site, when viewing the database through PhpMyAdmin or looking at a database backup with a text editor, do the local characters look ok?
3. After upgrading and using ’Set Names’, when you add a new document with local characters, do they appear ok on the frontend?

Yes, the problem was with wrong charset that looked ok in earlier versions. The Swedish latin collation (for some reason a default for mysql databases).
Thanks.