Only a little. My personal experience is that the only transfers that have gone smoothly and quickly are ACAT transfers of a) entire retirement accounts that b) consisted entirely of mainstream mutual funds. I've done several of them (I'm fickle with brokerages I guess) that have taken, oh, much less than two weeks.
However, my transfer from TIAA-CREF ("annuity" accounts) to Vanguard, where the things being transferred weren't mutual funds, took something like seven weeks. And a couple of attempts I've made to do partial transfers--nothing complicated and nothing but plain-vanilla mutual funds, but not the entire account--in both directions, between Fidelity and Vanguard--went through complicated cycles of not completing and being restarted and fresh authorization forms. Most amazing, it once took well over three weeks and three or four telephone calls to transfer about $1,000 in a money market account from my Fidelity-managed 401(k) to my Fidelity rollover IRA.
In other words, yes keep on top of it, but don't panic. I am sorry to say that during the slow transfers the reps were never really able to give me clear, detailed, or accurate information on exactly what was happening. I agree with livesoft that about one telephone call per week is about the right frequency, and, of course, record anything resembling a reference number or anything that will help the next person you talk to get to the screen that shows them everything that's gone before. Don't bother expressing impatience or annoyance.
In this forum there have been many stories of people upset because transfers took many weeks, and during the time the money appeared to have simply vanished, and nobody could tell them where it was--but to the best of my recollection the outcome, in every case, was OK.
By the way, this is why I personally feel that one should always ask for a "transfer in kind" whenever it is possible.
(Parenthetically, it reminds me once of what I learned about check clearing. It appears as if there is no such thing as a check clearing--that is, you can never determine whether an individual check has actually cleared. All that can possibly be learned for sure is that a check has NOT cleared. Everything else is just a reasonable presumption based on elapsed time.)
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.