[quote]How worried should I be?
“The mbstring PHP extension was not found and you seem to be using a multibyte charset. Without the mbstring extension phpMyAdmin is unable to split strings correctly and it may result in unexpected results.”[/quote]
It’s really hard to say how, or even whether, this will create any problems for you.
Note that the version of PHP that runs by default on the DreamHost web servers does have mbstring enabled (the MySQL databases and phpMyAdmin run on different machines).
I believe that you should be fine as long as you were able to execute your initial installation related SQL queries without problems, as the code interacting with your database on a day-to-day basis is running on a machine that has the mbstring extension installed.
I think that any potential problem would only be related to the use pf phpMyAdmin for activity outside the normal scope of operating phpBB, but it would not hurt to get an official answer for this question from DreamHost support.