I have an older dog (12 years) who has always been very clean and does her pooping in the far corner of the yard. Fairly recently, she has taken up the habit of pooping right in front of the gate, so that we cannot walk through the gate without stepping in it. And... she has stepped in it several times herself. Why is she doing this and how can I stop her?

Try not cleaning up the corner that you want her to go to. If you keep a few piles in that area, she may follow the scent and potty there.

At 12, there is no guarantee that will work. Older dogs get senile, just like older people. I would just suggest to stay on top of pick up and watch where you walk ;)

Yes, and move the poop by the gate as soon as she goes, and forgive all her old age failings. Soon she may not be able to control where she goes at all, including in the house.