Thank you for the log, Soizic.
While I don't see anything that indicates why the size of your preview window isn't being saved and restored, I do see that the Default Catalog on your system cannot be found. Did you remove it or move it to a different location? If you don't want the Default Catalog, be sure to go the Catalog Management window, expand the management interface (click on the triangle to the left of the Default Catalog in the Local Catalogs list) and use the Forget button to let the Catalog system know that you don't want it.
As for the preview window position and size, are you noticing that any other windows aren't saving and restoring their positions as well? All window positions and sizes are stored in a file called com.camerabits.PhotoMechanic.plist which is in the following location:
~/Library/Preferences
You can get there by copying that path and going to the Finder and using the "Go to Folder..." command on the "Go" menu. Then paste the path into the text field and click the Go button. Then find the com.camerabits.PhotoMechanic.plist file and rename it by adding a letter (I use 'x') at the start of the name.
The file should get created again and I expect things to start working. If they do not, please let me know.
-Kirk