When I load the EXE produced by FASM (format PE GUI 4.0) - the OLLYDBG gives strange message box:

"...The module... has an entry point outside of code... "

EXAMPLE in FASM has both data and code in same section, and ollydbg assumes its data section, so it warns about code being not inside code section.

Also FASM does not set Base Of Code and Base Of Data fields in PE header. Privalov?

These fields are only for some kind of "compatibility" with COFF format and are actually obsolete (Win32 doesn't use them). The very first versions of fasm's PE formatter were filling them, but then I've decided to remove it, as it's actually impossible to determine that value in case when you can put any sections in any order (for example two data sections interleaved with two code sections).