Well first off Alben W. Barkley would become President. He'd probably serve out the remainder of Truman's sentence, but just like OTL the labor unions would probably consider him to old to run in 1952 and pull support for him, so it would create an open race.
Barkley probably would not have pardoned Oscar Collazo, who would most likely have been executed as he got the death sentence for assassinating Truman.
Not sure how he would have handled the Steel Strike of 52 or if he would have created the CGCC in 1951. The one difference between Barkley and previous VPs, is that he was the first VP that was considered a part of the President's Cabinet, so he would have been more prepared than say Johnson was when he took over for Lincoln. He was a staunch supporter of Israel, even more so than Truman.