I have used Duolingo for other languages, and I've now briefly tested it for Latin.
There are two major issues:
It goes way too fast.
If the course has to be short for practical reasons, I would much rather have it stop early than go fast.
The system is too inflexible at accepting translations in both directions.
I am not sure if you can even reasonably enumerate all possible phrasings of a complicated sentence.
As VladimirF mentions in a comment, Duolingo does not have the capacity to understand structures more flexibly.
(This feels similar to the issues with Google Translate which appears to have no structural understanding.)
By the second lesson you encounter the first three conjugations, datives, vocatives, ablatives, several pronouns, and more.
I don't think you're given enough time to understand the structures before new ones are thrown at you.
You don't necessarily need full theoretical understanding to move forward, sure, but the pace feels counterproductive to me.
First handling basic structures with care would be great; I would be happy to see only first declension feminines for the first two lessons.
It appears that the rate at which new grammatical ideas are introduced is very high at first but then declines.
Errors in spelling and minor details will probably vanish in time.
What can be much harder to cure is the acceptance algorithm.
There can be many ways to interpret a phrase, and the program can force a narrow and possibly unnatural wording.
I have seen this with other languages, but I already got the feeling that it will be worse with Latin.
For example, Quid agit Marcus? had to be translated as "How is Marcus?" whereas "What does Marcus do?" was wrong.
Similarly, Me male habeo is allegedly "I feel poorly" but not "I feel unwell".
(This changed after my feedback. To improve the system, flag your good answers that should have been accepted.)
And as cnread comments below, the system can force a word order in Latin when it is free and the forced one might not even be very natural.
I think the Duolingo can support studying Latin, but it seems to make a bad only teacher.
I just completed the entire course (I wrote the first version of this answer after a couple of lessons), and I must say I am quite unhappy.
In addition to the two major issues I discussed, I dislike the focus.
The vocabulary is weird and often unnaturally translated, and the focus on modern United States feels very artificial.
The sheer amount of poop and drunken parrots shows bad taste to me.