You can rotate the appearance of photos in the contact sheet or preview window by using the arrow buttons. You can also select and rotate multiple photos through the Image menu. 

Rotations in Photo Mechanic are "soft rotations," done through metadata.  

Many cameras have a sensor for camera orientation that saves embedded metadata (EXIF) in the photo. Photo Mechanic uses this EXIF orientation data (if available) when displaying your photos. 

Rotating a photo in Photo Mechanic will only change the EXIF preferences. If you open a photo in other software, it may or may not read the EXIF data, so you may find that photos have "lost" their rotation when you open them in image editing software. 

Apply Rotation to JPEGs...

Although Photo Mechanic rotations are soft rotations done through metadata, you can force a "hard" rotation on JPEGs by re-writing the pixels to the desired orientation using Tools>Apply Rotation to JPEGs... Once you do this, your JPEG photos will appear in the same orientation in other software.