Okay guys, I finally have a few minutes.
I had an audio interview last year that I recently posted a link to:
http://www.audiocircle.com/index.php?topic=102655.0In the interview I was asked about first order crossovers. My response was very similar to much of what Turbo has just mentioned.
To further expand on that subject I will add a few thoughts.
In theory there are advantages but rarely is a designed executed in such a way that there are not other problems that negate all or part of the original design goals.
Here is a good example. This is a Spica TC-50.

See what the upgrade that I designed for it involved and how the crossover was changed. See before and after measured responses too.
And for what it's worth, my A/V-1 speaker (compared side by side) imaged much better despite the time alignment of the drivers in the Spica.
Typically I see a speaker using first order slopes and claiming to have time aligned drivers and all the befits that goes along with that.... but then the surface reflections of the front baffle create the same time delayed reflections that they think they got away from with the first order crossover.
At least the Spica did cover the front baffle with felt.
Also note the example shown and its measurements regarding off axis response. The measurements really tell a tale.
Keep in mind that what we really hear is a combination of the speaker and the speakers interaction with the room. Some call it a room response or power response. This is typically where the first orders slopes cause problems.
The gradual roll offs of the woofer into the tweeter and tweeter into the woofer means a lot of overlap or both drivers covering the same areas. When this happens you can wind up being in phase on axis and have a smooth on axis response. But then just above the tweeter axis they may be very out of phase. This is especially true in the upper ranges.
Let's say that the crossover point is 2,500Hz and first order. The woofer is only 12db down (or less) at 5kHz. At 5kHz the wavelengths are much shorter and just a slight phase rotation (change in driver alignment) will cause cancellation.
So there is a hole in the vertical off axis up and down and that un-even response will be reflected in the floor and ceiling reflections, and especially in the ceiling reflections So the in room response may look rough even though the on axis is advertised as very smooth.
Now you can get away with using first order crossovers very effectively in the ranges below 200Hz. Down here the wavelengths are so long even extreme vertical changes only cause a very slight phase rotation.
I could cover a lot more on this but Turbo covered a lot of it very well already.
More to come...