It appears that quests disappear if I load a previous save game.
This doesn’t always happen but it often does.
Example: I got a pirate quest to hide money for them. I accepted and they stored the money.
The quest said they would be back later to claim the money and give me a cut.
Several minutes later I reloaded the game and the quest disappeared. I still have the money. I’m assuming that it is now mine to spend.
This has happened with various quests. I get through some or all of the requirements and reload a saved game and the quest is gone.
Hm, we have not been able to reproduce it unfortunately.
Could you try saving your game before you get any quests, and then enable developer mode in the settings, use F3 to cheat in game, give yourself a quest, save and load, and see if it’s reproduced?
If you can do that, sending us both saves would help us a lot in tracking down the issue!
I found this issue as well.
Also where is the combat mode button? 
Sorry for the late answer @Astatroth, I was on vacation. The combat mode button should be in the top panel.
I suspect there is a bug in some screen resolutions that hides the button. If you can’t see it, post a screenshot of the problem.
Sorry about necroposting but I have experienced this bug or one that appears very similar in the latest update (graphics update beta 1).
I believe I can add a little information to help you track it down. If you save whilst you have a quest then load that save, the quest is ended (failed?) when loading has finished. You may see the quest in the list of notifications near the upper right before it disappears. If you however exit/restart the game, then load the save, the quest will continue normally.
Sorry for the late answer @Dusty_Monk.
Thanks for the report. This has to be a different bug and is probably specific to the quest type. With which quest did you experience it?