Some of the reactions to my earlier post, like Paul Krugman’s, have been that we no longer teach Textbook Mundell Fleming (TMF), but instead teach something along the lines I was suggesting. Which is great.  Of course I never meant to suggest everyone is taught TMF, but enough are to make the post warranted.
Another line, which I attempted (unsuccessfully) to head off in the original post, was UIP does not fit the data, so why build a core model that uses it? There are three replies to this:
1) Although UIP does terribly in the short run, its deficiencies in the longer term may not be so bad. Menzie Chinn sent me a summary of his own work that suggests this, which is here. In my two period model, where the first period is a Keynesian short run, then its the longer term predictive power that is relevant. Having said this, I also in my lectures stress that UIP is not well supported by the data, and that some people believe you can make money by betting against it (e.g. the ‘carry trade’).
2) However I do not think there is a more empirically based alternative that is satisfactory. Some people suggested a random walk for the exchange rate, and indeed - as Nick Rowe points out - we can recover TMF from UIP this way if expectations are formed on that basis. But a random walk model is inconsistent with almost any macroeconomic theory involving exchange rates that we might care to teach.
I know many people react negatively to rational expectations, but really all I’m arguing for here is common sense. Take again the example of a temporary (first period) fiscal expansion in a two period model without any backward dynamics. Unless the model contains hysteresis, we know the second period exchange rate will not change relative to the no fiscal expansion case. So to assume that agents expect any change in the first period exchange rate to carry through into the second period is the height of irrationality. I really do believe we should not be teaching models to undergraduates where people are that dumb.
3) Its what macroeconomists use. I know many people do not like this, but I have always felt strongly that the core of first or second year undergraduate macro should be consistent with the macro that, say, central banks use. It is bound to be simpler, but it should be consistent. Of course we should emphasise its deficiencies, and mention alternatives, and also generally say something about the history of how we got here. The problem with too much undergraduate macro is that it is history in the wrong sort of way - its just out of date. 
In my earlier post I tried to emphasise the inconsistency between TMF and UIP, and not go on about the fixed money supply assumption. However, just as teaching up to date macro involves using the IS part of IS-LM along with, say, a Taylor rule, so it should be possible to adapt TMF to a world where central banks set interest rates if the model was any good. Yet if we dropped the LM curve from TMF, and assumed instead that interest rates were the policy instrument, we would conclude that an independent monetary policy in an open economy with flexible exchange rates was impossible. According to TMF, central banks cannot set interest rates to anything other than world interest rates. Why do we want to start students off with a model that suggests this?
And so finally to the LM curve itself. I have yet to hear a remotely convincing justification as to why this remains in the first macro model that we teach students. What great insight do students get when we pretend that the central bank fixes the money supply? I’ve talked about the muddles teaching the LM creates before - David Romer presents seven advantages of doing something more realistic here.  Is it really the conservatism of textbook writers that means that we are condemned to carry on confusing students, and cannot we do anything about this?
 I always recommend students read Krugman, Obstfeld and Melitz when they get confused about open economy macro, but I had my sights trained on other macro texts.
 Yet I do teach a backward looking (static expectations) Phillips curve alongside a New Keynesian Phillips curve (NKPC). Why the double standard? I can suggest three reasons: (1) using static inflation expectations is not so obviously silly if the monetary authorities give us little clue about what they are doing, which describes the world a few decades ago, (2) there are empirical features (e.g. Phillips curve loops) which are difficult to rationalise with the NKPC (3) firms and workers do not spend large amounts of money trying to predict future inflation.
 So, for example, I’m happy mentioning TMF as a lead up to UIP. Saying something like “originally economists modelled capital flows as a function of only interest rate differentials, but this either ignored expected capital gains, or made a very naive assumption about exchange rate expectations. We now know better.” For much the same reason you might mention that the original Phillips curve did not have an expected inflation term in it, but we now know better.
 Oddly, although Romer carries through his arguments to an open economy, he does not embrace UIP: in fact I do not think he even mentions it.