WARNING!! Some of my understanding might stil be wrong as I only read the rules a couple of times so far. If I talk nonsense, please feel free to correct me in the comments section. I want this article to be as accurate as possible in the end. Thank you!
Movement in Team Yankee is very quick compared to Flames of War. Generally speaking, Dash (TY for Double Time) speed has increased all across the board. Moreover, going over Terrain either hinders your movement very slightly (when Dashing) or not at all (when moving at Tactical).
Also, basic movement distance for Tanks is increased to 14" while for infantry to 8". On the other hand, Tactical speed for light armored vehicles has dropped to 10'. This overall movement speed increase is coupled with easier unbogging. You no longer have to roll a skill test to unbog. This simply happens automatically at the end of the turn in which your tank got stuck.
A completely new thing is Aircraft Unit movement which has no range limit or can take the Aircraft Unit off the table to come back during one of the following turns (Loitering Off Table - p. 30).
Command Distance is now 6" (or 16" if you are forming a line and are in LoS of the Unit Leader) for every type of Unit while penalties for breaking Command Distance have decreased. The isolated part can go about on its own using Tactical speed and only suffer a +1 to hit. If they decide to stay in one place, the penalty is not applied. I doubt, however that anybody would be using this rule to divide their platoon into two parts and operate independently or go Line Abreast as Morale checks are based on what Teams are around the Unit Leader (the more Teams you have, the safer the platoon is).
All this combined, means that Teams in TY can cover a considerable distance in short periods of time, while staying relatively close to one another. I really cannot make my mind if this is a good or a bad thing. What I am sure of though, is that tables will suddenly become very small and artillery more effective :)
The biggest change that the designers created is the introduction of Movement Orders. Movement Orders can be used by a Unit Leader (in case the Unit lost their Leader- they obviously cannot use them) to make the Unit perform certain activities on the battlefield. let's have a look on what is possible:
Blitz Move (p. 34)
The Order lets the Unit move up to 4" upon a successful skill check. At the same time, it does not count as having performed a Move. This has major influence on the game. All of a sudden, your move or fire weapons can pop out from behind a LoS blocker and shoot their weapons. It will be the modus operandi of ITV vehicles or Soviet BMPs, provided you can succeed with your skill check. If you fail the roll however, you will suffer a +1 to hit penalty and will not be able to Dash.
What is more interesting is that this rule can be used to bring your Units out of reserves (confirmed by Phil) and IN MY OPINION, BASED ON RAW even return your Loitering Aircraft Units onto the table (p. 30 - as it can be used 'instead of moving'). In both cases, you could for instance use it to bring Cobras onto the table and shoot their move or fire rockets.
In the previous article, I mentioned that joining Commanders to Aircraft Units can be beneficial to them in some cases. This is one of them: if you join your pretty much useless Mech Commander to a Cobra Unit left in the Reserves, you can improve their skill check from 4+ to 3+ to Blitz onto the table and use their rockets. Not a big bonus, but can make all the difference.
Follow Me! (p. 34)
The Order enables the Unit Leader to move forward 4 extra inches (even after making a dash move) and roll a courage check. If successful, teams from the same Unit, within 6" and visible to the Unit Leader may move up to 4". Whether the Movement Order was carried out or not, the Unit is not able to shoot in the subsequent shooting step. This is not a game changer to be honest and I expect it will be used mainly as a way of getting into assault quicker. Also, it can be used once in a while to gain some additional ground while dashing and maybe in 1/100 games to increase the Tactical speed of a Unit to do a last minute objective grab or a contest.
Shoot and Scoot (p. 35)
This one is essentially a limited copy of German Stormtrooper move that we know from FoW. It enables a Unit that did not Move in the Movement Step to roll a skill check in the Assault Step and move 4" if successful. This is obviously a good way to limit the return fire of enemy Units and will be often used by vulnerable Units such as ITV vehicles, Artillery and AA.
Cross Here (p. 35)
As we already know, bogged down vehicles unbog at the end of the player's turn in TY. To make bogging down even less annoying, BF decided to introduce this new Movement Order. It improves your Cross ability by 1, provided your Unit Leader successfuly crosses an obstacle and you forfeit your chance to Shoot or Assault this turn. The bad part is that you only declare it BEFORE the Unit Moves. This means that you will almost never use it anyway as it costs you the Shooting and Assault Steps and you are not even guaranteed to have the improved cross check.
Dig In (p. 35)
Dig In only changed a tiny bit between TY and FoW. The two differences are: you need a Unit Leader to do this and you cannot fire bombardments after digging in. What might be the hint for the future releases is that currently, there are no Infantry Units able to deliver bombardments :) This rule, combined with the Blitz Move also have a small gap in it. By RAW, when you are Blitzing, you do not count as having moved your Unit. The Dig In order lets you use Foxholes until you move. These two rules combined mean that by RAW, your Dug In infantry can Blitz around the table in their Foxholes. Fun.
Overall, I like what BF did by introducing Movement Orders. It took away some of the nationality flavor that we know from FoW (everybody knows German Stormtrooper :) ) but introduced so many new possibilities!