MAX MAP BRUSHSIDES
MAX_MAP_BRUSHSIDES occurs when your map exceeds the VBSP 19 maximum defined brush amount.
The current limit is 65536, this is due to the VBSP 19 format using 16-bit integers (also known as "shorts") to count the number of brushsides. The maximum value of a 16-bit unsigned integer is 65536 (2^16), hence the limit.
There is no fix for this without altering the BSP format and possibly breaking compatibility.
Hammer/Compiled brushsides discrepancy
The term "brush sides" is a bit misleading, if you've paid attention to your brush sides in hammer before, you may have noticed the compiled result was higher.
This is because when compiling, it includes the bounding box of a brush, which can be up to an additional 6 brushsides per brush. If a face is lined up with the edge of the bounding box(meaning not angled in any way) it will not add an additional brushside.
Example: A 5 sided pyramid shaped brush with the bottom face lining up the bottom of the bounding box. While the brush itself is only 5 sides, it will count as 10. The 5 extra brushsides come from the bounding box.
As rule of thumb for figuring this out easier. 6 + angled faces = brushsides per brush