#1 is nothing. She is just being controlling.
#2 is serious - you really screwed up. Been there done that
So whereas you shuld appologise for #2, buy flowers/chocs etc., for #1 you should tell her to knock it off in the most macho way you can muster.
Dangerous advice, b/c the response to #1 is basically saying, "What is important to her is NOT important, so just ignore it." Talk about taking the fast train to resentment.
Just because cleanliness/orderliness may not be important to one person does not mean the other person is "controlling." One of you might be a truly disgusting slob; the other might be an obsessive germophobe. More likely, however, one of you is male and the other is female. What "does not matter" to him is often part of her core self-image. Ignore it at your peril!
There are many approaches to this issue, but one of 'em is not "let the other person know that what matters to her is not important."
You can compromise a lot on an issue like this--just make sure you let her know you value what is important to her (even if you don't share that degree of concern) and LIVE UP TO whatever agreements you make. If you have agreed (and silence means consent) NOT to show the room, then live up to that agreement. Invite the friend back to see it another time, and clean the darn space before then. If you know you will be wanting to show someone something back there, then let her know and ask what the two of you can do, in the time you have, to make it presentable.
You might bluster your way into intimidating your wife into letting you win (by macho behavior), but you will be losing. S*it on enough things that are important to her but that you "judge" to be insignificant, and you are sending a very clear message you do not value her. Take the time to discuss, understand, and work with what is important to her, and you build a stronger relationship.
So, for #1, apologize for not taking her need (to present a clean home) seriously. Let her know you won't do it again--you will plan ahead of time if you might want to show the room, or you will make plans to show it later, when you've had a chance to straighten it. Or, you will unbolt the item and bring it out rather than sacrifice her request to indulge your own passion. Ask her if any or all of these are acceptable options. Expect her to be surprised and pleased that you "get it." Keep up the good work.
Edit: just saw your post about how these are old things. A lot of people will say that she is "wrong" for bringing up old grievances. But that ignores the much more important reality--they are windows into her view of the relationship AND they are moments when she experienced a paradigm shift in her understanding of the relationship. She is giving you two VERY clear examples with a common theme: she feels you do not give her needs and feelings very much consideration when you are making decisions. It sounds like you might be very impulsive--so this lack of consideration may have happened a LOT. You probably do not intend to "slight" her feelings/needs, you are just being "you," excited about the plane, excited for your daughter. . . she is warning you that she is having trouble with "you." IF you have impulse control issues, she may learn to understand that your ability to stop and consider her needs is limited. Right now, she thinks you do not VALUE her needs/etc, and your impulsive behaviors are a conscious disregard for what is important to her, a conscious assertion that what you want is more important than what she might want/need, time and again.
Impulsive behaviors can come across as simple thoughtlessness--you did not take time to think about her b/c she is not important enough. Or, she may think that you are doing it intentionally, a passive aggressive response--b/c she has let you know certain things ARE important to her. If you are quite sure that neither of these things is true, and maybe you really have an impulse control issue, then explain that to her--and regardless of whether her thinking is fairly accurate or not, try to do better at ASKING her before you make decisions about things you are going to do. Asking for her input shows you value her concerns and her judgment. If you do it a lot of the time and then forget on occasion, she probably won't even notice (once her resentment wears away for all the past offenses, which could take a while b/c she has to see enough to let her trust that you really do care for her needs/judgment, etc.)
Sounds like you are making progress at getting her to open up. She really needs to work on this problem of conflict avoidance, of course, so encourage counseling for the two of you. Good luck.