The 1/3 turnover every 2-yr and 6 year term of the Senate is pointless. Legislatures are partisan and the upper chamber is no exception. The only difference should be the base of representation (population for the house, states for the senate), not some fancy prestigious filibustering club that slows everything down just for the sake of it.
The House and Senate working together to pass identical legislation is an inherently deliberative process. The Senate needs to lose some of its inefficiency.
I think the main problem of this is the filibustering you mentioned, and the fact that you need at least 60 Senators to get things done. Short terms wouldn't change that.