Over the years, I've added almost 500 contacts to my network but it has been ages since I worked with most of them. I recently located a contact in a target company and we were related to a mutual contact who I requested to introduce me. It turned out that my friend worked with that person a few years ago and has been out of touch. It would be useful if LinkedIn shows a recency indicator for each connection. Users can use that either as a reminder to reach out and strengthen the connection or to retire the connection over a period of time. Fewer strong connections are more useful than many weak connections.
"Jobs you may be interested in" - only the 8th job opportunity suggested is the first one in my location. Tweak the prioritization of results to weight local jobs higher, perhaps run an A-B test to measure conversion. Along that same vein, if I've run keyword searches in the past, factor that into the recommendation. The current algorithm appears to disregard that, making the list less interesting.