I have complained before about IS-LM being the first macromodel most students encounter, when no major current central bank fixes the money supply. The textbook version of Mundell Fleming (TMF)  is the first, and often the last, short run open economy model students are taught, and it shares the same deficiency. However the problem with TMF is even greater. It is inconsistent with Uncovered Interest Parity (UIP), and if we use modern macro as our yardstick, this makes it simply wrong.
Lets take a topical issue: the impact of a temporary increase in government spending. We should be immediately worried that TMF makes no distinction between temporary and permanent increases. It says both have no impact on output. So every student learns that fiscal policy is ineffective under flexible exchange rates. For a temporary increase in spending this is incorrect.
The logic of the TMF proposition is usually demonstrated by shifting various curves, but it is in fact trivial. In TMF money demand must equal a fixed money supply. If money demand depends on prices, output and interest rates, and the first is fixed in the short run and the last is tied to world rates, then output cannot change either. This complete crowding is achieved through an appreciation in the real exchange rate.
But why should domestic interest rates equal world interest rates? UIP tells us they need not. A temporary increase in government spending will raise output, which given a fixed money supply will raise interest rates. This will lead to an appreciation, but the temporary nature of the shock means that the long run exchange rate is unchanged. So the current appreciation implies an expected depreciation, which offsets the additional return offered by higher interest rates. The result is a short run equilibrium where output and domestic interest rates are higher. There is partial crowding out through an appreciation but not full crowding out.
Now you might say what is so great about UIP. But at least UIP is based on something: a simple arbitrage theory. As far as I can see the TMF assumption that domestic and world interest rates are equal has no equivalent foundation.
We only get some crowding out in the experiment above because the money supply is fixed. If interest rates are fixed instead then we get none. With fixed interest rates, UIP implies the current exchange rate is unchanged when government spending increases, so there is no crowding out. We get exactly the same result as with fixed exchange rates - the complete opposite of what TMF suggests.
Now you might plead in mitigation for TMF that at least it gets the impact of a permanent increase in government spending right. I think this is a very weak defence. A permanent increase in government spending, assuming it increases aggregate demand, is crowded out because in a small open economy the real exchange rate equates the demand and supply of domestic output in the long run, which is a more basic result than anything in TMF. 
Another weak defence of teaching incorrect theories is that they are simpler than better theories. However it we combine this basic idea about the determination of the medium/long run real exchange rate with UIP, we have a complete theory of the small open economy which is no more complicated than TMF. So why does TMF survive?
Perhaps one reason is an addiction to two dimensional, and preferably static, diagrams. Yet the system I’m describing can be represented by just two equations and two periods. The first equation is the familiar aggregate demand curve. It is static, so we have
y = f ( g, r, e )
where g is a shift variable like government spending, r is the real interest rate and e is the log of the real exchange rate. Use stars to denote second period (medium/long run) values:
y* = f( g*, r*, e* )
Now here I can say that r* is equal to the world real interest rate rw (because of UIP and a constant real exchange rate), and y* is determined by some classical supply side, so this equation determines the second period real exchange rate - the basic result I mentioned above. The only other equation I need is UIP:
e = e* + rw - r
where e is defined so that an increase is a depreciation. Policy determines the short term domestic real interest rate, and therefore the short term real exchange rate.
The aggregate demand curve is already familiar to students, and the adaptation to an open economy is intuitive. UIP is easy to teach: any interest rate differential is offset by expected capital gains or losses. So it seems to me something like this should become our standard introductory short run open economy macromodel. And TMF should disappear.
 It is well known that in open economy macro everything important must have a three letter abbreviation. It is a basic result that may be inconsistent with PPP, but that is another story.