Please be aware that all of the statistics and performance discussed in this post reflect the version of the ship as she appeared during the testing period.
In short, Mutsu's gun handling and rate of fire was buffed rather significantly. This in turn greatly affected the DPM we saw during play testing. This put her optimal DPM down to 170,057 AP damage and 89,143 HE damage. The buffs provided by Wargaming increase her DPM by a full 17% which I think we'll all agree is enormous.
The Nagato-class has never been considered a heavily armoured ship and the deficiencies on Mutsu only exaggerate this weakness. While she can angle against 356mm rifles, if she doesn't angle properly she can (and will) get citadelled with alarming regularity. Her citadel sits over the waterline and while her belt armour and the turtleback protecting these machine spaces looks formidable, these are often bypassed by shots striking her from range, which need only contend with the 25mm + 70mm deck armour found amidships and the pathetic 25mm roof her citadel. She has objectively worse protection than the Warspite at all ranges.
Wargaming didn't want a repeat of the German Destroyer incident. They let us Community Contributors know in advance that the Mutsu we were playing wasn't the final version. There were all of three changes that they gave us, but let me be be clear -- there may be others. As values like vertical dispersion, Krupp and shell-drag coefficient are not intended to be public knowledge, there are lots of parameters that could still change before release. So while I appreciate Wargaming striving to keep us in the know about what the release version of the ship may be, it pays to keep that disclaimer at the top of this article in mind.
Mouse: Well I liked her. However, I don't think I would play her very often, not compared to the other premiums 6s.
Lert: She handles comfortable enough, if a bit sluggish on the rudder. I would consider her a fun ship if her shells didn't tend to shatter at long range, or her hull held up a bit better under fire. Plus, her torpedoes are just funny, if you get a chance to use them. Those are big if's though.
GrafZeppelinKai: I enjoyed my time testing Mutsu. To me, the gunnery felt familiar and comfortable, and you can never resist a giggle when you surprise an adversary by pooping out a torpedo.
Don't skimp out on the premium consumables for this ship. Taking a premium Damage Control Party is an absolute must. I also strongly recommend taking a premium Repair Party as well to reduce the reset timer of your healing potion and to give you an extra charge. I don't see much need in breaking the bank with a Spotter Aircraft, so it's up to you to invest in the 22,500 extra credits to make this premium or not.
After this first pass, there are other skills to consider. The best of the bunch are Adrenaline Rush and High Alert at tier 2 and Superintendent at tier 3. This is one of those rare ships where I will not recommend Basic and Advanced Fire Training as the top picks. While these will help prop up her horrible AA firepower, it's really not going to move the needle enough to make it anywhere near acceptable. Similarly, her secondaries are just a little too short ranged to be worth specializing into. You can certainly try it out for yourself, but I don't think you'll find it pays off as well as it would for her tier 7 sister.