I decided to try out the tutorial built into the game with Beta 4 (ver 0.95). Here are some of the issues I noticed. Not all of them are necessarily problems that are exclusive to the tutorial (for instance, the quest text issue is probably seen for that quest in general, not just in the tutorial); I stuck issues like that on the end of the list.
1) Attempting to load a saved game from the tutorial crashes the game. This includes autosaves made by FE. The tutorial's short enough that disabling the ability to save (and disabling autosaves, of course) while in the tutorial would be a viable solution, but if you make the tutorial much longer, that would no longer be ideal.
2) When you collect treasure as one of the tutorial objectives, the pop up telling you what the next objective is (train a pioneer) shows before the pop up telling you what you picked up. This is annoying. (If I recall correctly, a previous version of the game was even more annoying: It the objective pop up was sandwiched between two other pop ups - one saying you went through the site and found an item, the other saying what the item is. Putting the objective pop up before both of these is better than that, but the ideal order would put the objective pop up after both of them.)
3) I researched Refined Production in the tutorial, but, when prompted to choose what to research next, it still showed as unresearched. I then selected the Training tech, and it was researched instantly, prompting me again to choose what to research.
4) Typo in "Recruit a Champion" objective text. The text "eastern forest your realm" should be "eastern forest of your realm". Also, it says "your newly found outpost", but you didn't FIND the outpost; you built it!
5) The spellbook interface in the tutorial videos seemed to be from a previous version of the game. There maybe have been other problems with the actual interface not matching that shown in the tutorial videos, but I didn't notice (perhaps because I'm not all that familiar with all the different UI elements yet).
6) If you use the middle mouse button to rotate the camera less than 180 degrees from the normal position, it rotates back to the original position automatically in an overly "dramatic" fashion, doing a near 360 even when the rotation changes you made were only a few degrees off from the position it takes you to. (There's probably an option to make it not snap back to that rotation at all; obviously if you're not seeing it automatically rotate back at all, you should disable that option and test this again.)
7) Quest popup asking if you want to do a quest shows rewards, but in the case of item rewards, you can't easily tell what they are. It'd be much better if you could put your cursor over the reward item (e.g. "Doom Club" text and the icon that represents it to its left) to get a tooltip showing the item's stats, etc.
8) Rats in the Ruins quest: The text in the popup telling you you've cleared out some rats gets cut off. It says "Return to the inn and" -- just like that, cut off mid-sentence. There's a bunch of empty space below it, and then the Done button.
I also have a suggestion for an addition to the tutorial that I think would make it much more helpful:
After you recruit the NPC in the tutorial, there should be an objective to group it with your sovereign before you attack the elemental. In fact, the tutorial really ought to teach you how stacks work in general. This element of the game is a bit confusing and should be explained much better - and not just through a quick line like "move your guy on top of the other guy and they'll stack". It should explain group size limits, dividing groups up, defenders in cities, etc.