Unless you want image search bots to be able to index the images on your site there should be no problems with the search engines at all.
If the partner doesn't have any objection to you hotlinking to the images on its server -- and using the bandwidth that goes with it -- it can save overhead on your server (just look at the properties for any image on this page to see how Brett handles it), and this can be important for a high traffic site with a lot of images.
You should also consider your partner's server performance. Are many other sites pulling images from the partner's server? Does it impact the load time of your pages? Etc., etc.
Other things to consider are. 1) The images will not load if their site goes down. 2) They will be able to tell what traffic you are getting on your site by looking at their logs for those hotlinked images.