The two most common mistakes are bass and treble

OK, so I know many of you will have a knee jerk reaction to that with something like "well you've just covered most of the spectrum!" but I mean to say more than what I can fit in a headline.

When first purchasing speakers the biggest regrets, or sometimes bad choices without regret, is looking for a speaker that is too detailed. In the store over 10 minutes it mesmerizes you with the resolution of frequencies you thought you would never hear again.  You take the speakers home and after a month you realize they are ear drills.  High pitched, shrill sounding harpies you can't believe you listened to long enough to make a choice.

The other mistake, which audiophiles life with far too long is buying too big a speaker for the room.  The specmanship of getting 8 more Hertz in the -3dB cutoff is a huge factor in speaker purchases.

What do you think the biggest mistakes are when buying speakers?
I feel so fortunate that the store where I get my Hifi gear lets you try before you buy. A few of my pieces of gear would not have ended up in my system like the Puritan PSM156 or the Nordost digital coax cable. I am excited because they have become the Ayre dealer in the Chicagoland area. Demoing gear in the home is the most important thing you can do. Even if you bring in your gear to the store it will not sound the same. If you are in the Chicagoland area and want to demo things right try:

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I’m coming from the perspective of engineering and as an amplifier manufacturer of the last 45 years

Within a specific power envelope ?

The other problem you deal with is of course that you get thermal compression if the speaker lacks efficiency. You can’t solve this by getting a more powerful amp

No, you can solve it by various aspects of speaker driver and crossover designi. I don‘t think anyone could state that the ATC SCM50 (85db/W/m) suffers unduly from thermal compression. There are many other manufacturers who are cognisant of the impacts of thermal compression and design their drive units accordingly.
Another prime example are my original Acoustic Energy AE1‘s, which are notoriously inefficient, but were designed specifically to combat thermal compression, having their voice coils thermally bonded to the aluminium speaker cones to dissipate heat.

They sound atrocious cold, and really need a bit of warming up before they begin to sound good; sounding better the harder you drive them. They love heat. Their lack of compression at high levels is quite astonishing, even today, and makes nonsense of the idea that thermal compression has to be a limiting factor in low efficiency speakers. Their ultimate performance is mainly constrained by the driving amplifier.
I apologize if I sound like this- I'm coming from the perspective of engineering and as an amplifier manufacturer of the last 45 years.
I've always respected your posts on these forums and have learned a thing or two along the way. You contribute to this forum in a way that makes people see you as an authority. Over time you have created an environment where people know like and trust you.
You are not only an accomplished engineer but a marketing master. It's no coincidence that you have nearly 10,000 posts on a worldwide website ripe with prospects and perhaps the largest percentage of target market tuned in right here daily.
On top of that you make a neat and clean product in the USA and get rave reviews and accolades on your upgrades and product support.  I've never considered one of your products because I don't like the unprotected chassis design. With young kids in the house and nothing being "off limits" it never made sense.
Finally, no need to apologize to me, I'm taking notes. Well done you've earned it IMO.