Would there be any issues installing a dishwasher in the area I have shaded red in the picture below?

Imgur (http://imgur.com/YAV5yEh)

I'm wondering if the oven or distance to the sink might cause any issues? Looking to find out before I go and buy a free-standing machine.

That is too far for the drain line. If you install it where you want, the dirty water will drain all the way back to the DW and fill the sump with dirty water. You MAY get away with a small flapper check valve but would need to install it next to the DW.

If I am not mistaken most of the new dishwashers has a built in check valves installed, open the link below and watch the youtube, Thanks.

John

https://www.youtube.com/watch?v=vnM-jH4fm2M

You're right, John... most dishwashers nowadays have built in check valves AND high loops piped directly to the side of the dishwasher. With that being said, oven is no issue and drain is a long run, but I've seen quite a few DW with drains that were further away and they had no problem at all. You should be all set to proceed, Rizzzzle!

Mark

Thanks lads

Is there a basement or crawl space below the kitchen?

If you use Air Gap, then water, standing inside long discharge hose between DW and AirGap will smell through the Air Gap

Milo