What is the standard error of measurement for teacher made multiple choice tests?
Harvill mentions an estimate by Lord (1959). Lord (1959) presents some data for the standard error of measurement for some moderately difficult cognitive measures. While there are many caveats (e.g., the estimate of the standard error is most accurate for scores around 50% and the estimates are based on tests that are neither particularly easy or particularly difficult with means in the .35 to .75 range), Lord provides a simple formula that can be used as a rule of thumb for predicting standard error of measurement in his sample of cognitive measures which performed quite well. 

$$\hat{s}_e = .432 \sqrt{k}$$

where $k$ is the number of items.
Alternatively, if you are interested in the mean correct on a 0 to 100 scale rather than the total correct, you can divide by $k$ and multiply by 100.

$$\hat{s}_e = \frac{.432 \sqrt{k}}{k} \times 100$$

When I plugged this into R for some sample values I obtained:

&gt; lord_approximation &lt;- function(k) 0.432 * sqrt(k) /k * 100
&gt; k &lt;- c(10, 20, 50, 80, 100, 120, 150, 200)
&gt; cbind(k, sem=round(lord_approximation(k), 2))
       k   sem
[1,]  10 13.66
[2,]  20  9.66
[3,]  50  6.11
[4,]  80  4.83
[5,] 100  4.32
[6,] 120  3.94
[7,] 150  3.53
[8,] 200  3.05


Of course, not all of this reduction in standard error of measurement is due to greater accuracy. Some of it comes from the smaller standard deviation in true scores that occurs when you take the mean of more items. Furthermore, these estimates are based on relatively well designed cognitive measures. Teacher designed tests may have slightly lower reliability and thus larger SEM.

References


Harvill, L. M. (1991). Standard error of measurement. Educational Measurement: Issues and Practice, 10(2), 33-41. PDF
Lord, F. M. (1959). Tests of the same length do have the same standard 
error of measurement. Educational and Psychological Measurement, 19, 233-239.