the problem is, zen-cart displays in login screen in admin section and also after few clicks in shop in the bottom (also I can't login to admin, as it prints something like "There was security problem...."):

1062 Duplicate entry 'b8ab59f60086ac45bd663780b50aa923' for key 1
in:
[insert into sessions values ('b8ab59f60086ac45bd663780b50aa923e17af253', '1286378678', 'YUJZ...(very long string)...aQS4u')]

Zen-cart is in 1.3.9g version after fresh install (also in versions 1.3.9a and 1.3.9f)

But on my computer - PHP version is 5.3.2, MySQL 5.1.49 (all 64-bit) it displays no problems - when I look into the session table, length of "sesskey" is 26 characters

but on hosting - PHP v. 5.2.2, MySQL 5.0.83 (32-bit)
length of sesskey (after type change to varchar(64)) is 40 characters - so with default type varchar(32) sesskey was cut to 32 characters

after that change, it works OK...so I thing this is a bug