Why are the objects that I draw in 3D not aligned with the current UCS? Sometimes when I move or rotate an object in the 3D enviroment, the command is not executed in the current UCS.

Hello, if you draw your objects with F8 on ( ortho ) you shouldn't have problems ( if you do your commands with a 3D point of view.
Notice that with the recent release that you have you can draw directly in the 3 dimensions ( x, y, and z ).
If you rotate your objects beware of setting F8 on and set an UCS comformably to your rotation.
With 3D objects I frequently use ALIGN  rather than rotate so I can also move them to the right place in the same command ( with the option of scaling them also ).
With the 3D align command ( egal to the 2D ALIGN command ) beware of giving three points and not 2 ( even if you think it's OK with 2 because in some case you will not obtain the right rotation ( it's noticed in the help ).
May be it's your case.
Ask for more, and have a good day.

Not sure what you mean by "draw directly in 3 dimension". Let me try to better explain my command execution process and results.
I have one box drawn, aligned to the UCS. I draw a second box with the 1st corner snapped to the corner of the existing box. I usually like the "length" subcommand  then I can choose the length (x), width (y) and height (z) for the new box.
I almost always draw "ortho on" when in 3D but thank you for clarification.
I then use the 3D rotate command, choosing a corner or a mid-point as the base point. I then select one of the three axis to rotate on using the Gizmo. The results is the rotation of the box, out of the UCS.
Interesting enough that the gizmo line that flashes when selecting  an axis from the Gizmo appears to be out of align from the UCS.
Graphics issue?
Thanks for reviewing my post.

Hello, it's good to share informations and/or problems with that interresting subject that is working in 3D ( I also have problems and questions without answers ).

 
What I mean when saying working directly in 3 dimensions is that with old release you could only work in x, y confomably to your UCS.
Now you can draw a line in X following the red direction, Y following the green direction and also in Z following the blue direction.
This is good but can lead you not working in the right direction ( and worse if you don't have F8 on ).
 

There is an option to "Ignore snapping objects negative Z USC dyn" in the "OPTION" menu / Drawing that may allow you working in 3D with a 2D viewpoint ( I havn't try ).
 
What happen to me is having my UCS changing automaticaly ( not my will, not my choise and making troubles ) when approching a 3D object.
It looks like it have to see with the "dynamic UCS" but I havn't done searches on this subject.
May be your problems have things to see with this.
 
3D is so interresting , so difficult and problematic is you start your dwg with wrong first steps that I switch to old and slow drawing methods not to have to redraw everything in the middle of the work.
I have only AutoCAD 2008 and so my informations can be outdated ( I think that the "old and slow methods" are still OK on recent releases and may be better before you validate your drawings ).

Well OK then, I really only draw simple stuff in autoCAD 3D for now, time to end this discussion for now. I will use the "align" command more often until I get a bit more experience, stumble across another solution or get "Inventor" to use for 3D.
Thanks for your input!

Another solution found today.
When rotating a 3D part, right click after selecting the part, choose "align Gizmo with current UCS".

Hello N° 3, I read your answer of 16:25 and I found that you were sad or frustrated. You should not.
The use of AutoCAD 3D is not the all day user capacities, and then you found a solution on your own. This is good.
A lot of things can be done. I learned AutoCAD 3D on my own reading the old R13 book + the PDF book that you can find now in : c\program files\Autodesk\ACADM 2008\Setup\Docs.
For my job tasks, I found solutions for : Topo survey, developing sheets of special parts etc...
AutoCAD 3D may not be the more up to date and friendly user software but if you push it ( and you ) to the limits it will be more than sufficient and efficient.