Fixed! I posted a new build, version 0.6.1, that should solve your problem.
This bug was caused by some changes I made to the way your game is saved in v0.6. Basically, it wasn't checking to make sure you had a weapon installed before trying to save the weapon, causing a crash. When you bought a new ship with two turrets you probably didn't equip both turrets (which is fine) and the game didn't handle this properly.
Please let me know if this fixes your error and thanks for reporting this issue!
NOTE: I posted a request for your error log but it turns out I didn't need it so I deleted that post. Please disregard that request