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How big of a problem is, if I put my fingers not in the suggested order? At the C and Dm chords I find it much easier to lay them down in reverse order. (3rd, 2nd, 1st)
I know that the ultimate goal is putting them down at the same time, but until I reach that, I prefer this method. 
@martinelgore
To play songs and be proficient with chord changes at tempo, your long term aim will be simultaneous finger placement. There are steps along the way and one of those is naturally sequential placement of fingers. Justin suggests 1, 2, 3. There are other combinations as you have found. None is right / better necessarily in an absolute sense. Your ultimate aim is eventually moving away from sequential placement.
To get there, developing finger independence and avoiding the hard-wiring of one and one only sequential landing of fingers, I suggest this practice tip to do in small chunks of time.
Form the chords you mention (C and Dm) go between placing the fingers down sequentially but in alternating orders.
1, 2, 3
then
3, 2, 1
then
2, 1, 3
then
2, 3, 1
or whatever combination you can think of.
It helps to train finger independence and will help to the ultimate aim of simultaneous placement.
Hope that helps.
Cheers 
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Playing along with chord changes from C to Em. Instead of lifting fingers to switch to Em I’ve been just sliding 3rd finger over to the second fret. Basically Em in reverse for 2nd and 3rd finger. Keeps my 2nd finger anchored. Not sure if that’s good practice but for now it seems to help me.