What is the check mark in "Image Capture" for Yosemite and how do you uncheck?

If you mean the little green circles with white check marks on the edge of photos in Image Capture, those mark the photos that are already in the target locations (which could be a folder, iPhoto, or Photos among other choices). If a photo is already in the destination, you presumably don't want it imported again.

I wound up having to restart the process. This time, the appearance of the checkmarks took place during the same time that the miscellaneous file information was filling in down the page. When I double-clicked on a photo, Image Capture downloaded that photo to my selected destination folder and opened it in Preview.

It may well be that Image Capture acts differently for the two us because my selected destination is a folder and yours is Photos. That probably has something to do with the mechanism Image Capture uses to invoke Preview. I can't even get Preview to open an image inside either Photos or iPhoto through the Media > Photos section of the open dialog; it goes through the motion of letting me select an image inside the interior structure of the Photos or iPhoto library, but then silently fails to open it. Given that issue, about all Image Capture can reasonable do is download the image to some default folder and open it there.

For me, the checks do appear for images already in the target location. The time they take to appear seems to be related to the number of images on the phone and the number of images in the target location. When I had only a few, the checkmarks appeared in short order, but these days I keep quite a few images on my phone, so I see the various bits of information appear in sequence -- first the file names and dates, then the images, then the other file info (size, aperture, etc.), and eventually the checkmarks from matching with the target location.

I don't think I've ever intentionally double-clicked and watched the results, so I tried it as an experiment. It did pop up an "Importing" message immediately, but the initial data acquisition process wasn't complete, so the import is taking a while. In fact, it has taken the entire time I've been typing this. Ill be back when it is complete.

I certainly didn't intend to imply that Image Capture wasn't useful. I use it all the time to offload pictures from phones and camera memory cards and occasionally to scan documents with my all-in-one print/scanner/fax. In all cases, my targets are Finder folders, never iPhoto/Photos except for testing.