I am 98% sure that the following bugs have all occurred under 1.06.19. This isn't an exhaustive list, but these are the ones I can remember at the moment.
When creating multiple sovereigns without restarting the game, sometimes previously lowered statistics for the previous sovereign are replicated for the new one, but no points are awarded. Often talents behave oddly in this situation as well.
Newly created sovereigns do not always appear in the sovereign list. Restarting generally fixes this problem.
Sovereigns with Adventurer and Tracker often can not equip either the traveling boots or the journeyman's cloak (or both). No cause for this is apparent.
[Sufficiently] Wounded squads lose their squad/party status on reload from save.
Units being built are sometimes lost when restoring from autosave (this might be because the autosave took place the turn they were built, after the queue was cleared but before the unit was created).
Unit move power from Warfare>Movement does not work (the one time I've researched it at least)
Buildings which can only be built once (per settlement/faction/game) can often be built twice in a row in the same settlement, even if doing so puts you into negative resources.
The Vengeance Coating has no (noticeable) effect.
There is no way to go from a city's list of caravans to the associated caravans on the map. Coupled with Caravans not appearing on the left hand side, this can be very irritating.
City's will often display the wrong owner, name and status (friendly, neutral, war) in their overhead caption and selection/card (the borders are usually right however).
In tactical battles animations will sometimes 'glitch' taking up to 45s to complete.
The mapping of mouse coordinates in 3D space to actual grid location is often incorrect. This happens more often (or is far more noticeable) in tactical battles.
Pathing for units does not attempt to take the shortest path in all cases vis a vis terrain costs.
Mousing over non-friendly units in a stack will often (always?) display the wrong card for every unit after the first/topmost in the stack.
Selecting a non-friendly unit in a stack will sometimes displays the wrong information for the unit.
When a city region is first established (the turn after the settlement is established), sometimes a champion may not enter the shop (the purchase button does not appear). Reselecting the unit usually fixes this. This bug also appears occasionally for Pioneers vis a vis the Establish Settlement button on open ground.
Casting Imbue Champion on a stack with more then one champion does not provide a selection dialog for which champion to imbue. The selection appears arbitrary (possibly the first champion in the stack list).
Units added to cities do not notify when they are healed, but rather when they are healed including the city defense bonus (often several turns after they would otherwise have been fully healed outside of the city).
Neutral Champions you can not afford will neither talk to you nor tell you how much wealth you need to possess to be willing to talk to you. This may not be strictly speaking a bug, but it's pretty annoying 
.
Non-"human" ally units (Spiders, Shrills, etc.) cost "human" population to build.
Summoning spells will sometimes "refuse" to work. The casting tile hilite is green, but casting the spell simply does nothing. Repeated spamming of the spell (sometimes as many as 20 times) will eventually get the spell to work (combined with reselecting and panning the map, etc.). I have no idea what causes this. I guess I don't summon enough. This may be related to the mouse coords to map grid mapping bug. This also occasionally occurs for enchantment spells.
You can sometimes recruit Neutral NPCs with Champions who are very far away (10+ tiles). In general the chat distance for a Neutral Champion seems somewhat arbitrary (but appears related to Moves).
It is unclear that Charisma effects champion recruitment. This makes determining if the charisma of the recruiter (the champion near the target neutral) or your leader is the deciding factor. Adding the charisma effect to the cost in a tooltip would help.
Diplomacy>Dynasties appears not to function. You can not negotiate for a spouse for your leader with another sovereign, regardless of the number of children they possess or their age.
Resource discovery techs do not appear to reveal resources in/around settlements you establish after you have developed the technology. Even if this is the intended behaviour, the techs in question should have their descriptions and rationale altered.
Temples of Essence do not appear to function.
In the Hiergamenon, when reviewing completed techs, the techs no longer list what benefits they will provide (buildings, etc.)
The Construction Yard sometimes claims to grant 25% faster construction time on its card, and sometimes claims to provide +20% materials. No idea which it actually does as I haven't actually built one yet . Empire/Kingdom bug?
You can not unload units at a harbor. If you have only a single beach tile on which you have built your harbor, you can no longer unload troops at that location.
Stacking is buggy. Units do not always join armies they stack with, and sometimes leaders of a stack will leave their stack behind when selected and moved. This behaviour has improved greatly in the recent patches, but still occurs occasionally in 1.06. The behaviour is much more erratic with transports.
Units which leave garrisoning a city have only 2 moves, regardless of what their Moves capacity may be.
Units stacked with an organized leader and then separated retain (for that turn) the organized leader's moves even if they do not move with him.
The AI does not speak Transport. They are the magical ether ships of teleportation to the AI. Perhaps that's not exactly a bug.
Tactical plotted movement will sometimes, but not always usurp control at the start of a tactical turn. I.e. if you have a unit with a preplotted move (usually because it didn't have the move to reach to tile you selected for it on a previous turn), it will sometimes, but not always, attempt to move to that tile immediately at the start of the next tactical turn.
Teleporting a stack on the strategic map which had a plotted destination will cause it to immediately start walking to that plotted destination once the teleport is complete (rather then clearing that destination).
Monsters and Ruffians can spawn inside the influence radius of your cities.
Alt-tabbing out of the game will cause a DirectX error crashing the game.
Sovereigns can have children with spouses they've never been in the same square with 8).
