Maybe I shouldn't have put this clip with peaking because it does not show the main problem - ghosting/blurring objects. I returned the camcorder to the only one Canon service in Croatia ("Photo-centar", Hondlova 2, Zagreb, Croatia).
They are trying to make a fool of me! They say that they don't see any "blurring or ghosting" and that the LCD is totally as good as those on the XL2, XH-A1 and many other camcorders too!!!!
I repeat again - I own both camcorders XL2 and XH-A1.
By my own estimation, on scale from 1 to 10, (where the SONY Z7 is 10) I give following ranking:
XL1s = 5
XL2 = 6
XH-A1 = 6
XL-H1A = 1!!!!!!! (with my indication - that it is the worst LCD that I have ever seen)

I hope you understand me better now.
What do you recommend me to do?
Does anyone know where (main Canon service in Europe?) can I mail my complains at that service center in Zagreb?

On this clip you can see better how it looks.
Pay attention to the car's wheel.

LCD on XLH1A ghosting and smearing on Vimeo

I don't know about anyone else, but to me it looks like NR1 is active, but you say it's not in an earlier reply.

When NR1 would be active - in the display would be shown the name of active custom preset.

Well it depends on if it's setup to display them. I don't have an XL-H1A... I have the XHA1 and have CP's to always display, and when they aren't active, "CP" blinks. On yours CP isn't displaying. Maybe they're different?

Cp is not displaying because is not active! And I have CP's to always display
I know everything about setup of XL1, XL1s, XM-2 (GL2), XL2, XH-A1, XL-H1, XL-H1s, XL-H1a!
I own XL2 and XH-A1!

Well then if that's the case, then the A1 & your XLH1 behaves differently, like I said above. Sorry, just trying to help. I'll quietly bow out of this now :-\

Thank you for trying to help.

That looks about what I expected as far as ghosting, I honestly think I may have gotten use to the ghosting in my camera but maybe it's not quite as bad as yours. I wish I had a solution that didn't involve buying the fu-1000 but honestly I can't think of one. (you could get a hd-sdi monitor as well I suppose...)

I was at the service center this week. They have changed their opinion. Now they claim that they didn't say that the LCD on the H1a, A1 and XL2 are the same quality. Now they say that LCD on the A1 and XL2 is much better than the one on XLH1/XLH1A/XLH1S! And that the LCD on the all XLH1/XLH1A/XLH1S camcorders are really bad and that there is no help!!!!

I did not take the camcorder back and now I am waiting to get new one! (And they say that LCD on new camcorder will be also bad!)

Five days ago, I finally got another camcorder (XL-H1) to try it on. (But not from service in Zagreb). I am absolutely satisfied with LCD on this camcorder. It is almost the same as the one on the XL2. That shows that I was right and that what they were claiming in Zagreb service is not true at all.
(Btw., after three weeks of waiting for the new camcorder, they've notified me today that I cannot get a new camcorder even if it has good LCD!!!!)

Here is the clip from XL-H1:
LCD on XL-H1 on Vimeo

and old one from XL-H1a
LCD on XLH1A ghosting and smearing on Vimeo

While it is not a direct comparison as your content differs, I will agree that the xlh1 clip you just posted does seem to be cleaner with much less ghosting. Watching the first clip you can clearly see the LCD leaves a remnant of the "edge" that you are panning to and from. It looks like and old fashioned LCD that was way too slow, or, like my XLh1 when shooting in 32 degree or lower temperatures.

So what are you going to do at this point? The dealer/Canon won't get you a new one? To be clear, the EVF on the H1 series really does stink, but apparently you got one that is even worse than normal! But even when it is working right, it pales in comparison to other cameras nowadays.

Good Luck.

I forgot to write on this forum what happened at the end of "the case" LCD ghosting!
After waiting 3 weeks they told me that they can not get new camcorder.
I did not want to take back XL-H1a and I was shooting entire season with old but good XL2.
Now, I finally bought a Sony HVR-s270. (LCD & VF are much more better)

That one & only service in Croatia is really bad commercial for Canon!