When dealing with equations and data, typos are a common problem. In the following, I have pointed out several.
This is my primary reference for 25 (of 30+) equations. In order to reduce the number of typos, I used the provided Fortran source code and made only simple modifications to convert it to javascript.
When a value over ice is requested, the associated code replaces the result with HylandWexler (water) for any temperature above 0°C. I have elected not to do that in my code.
In the 2011 version, the Wexler over water formulation contains 2 errors, both fixed in a 2014 version.
 4.4412543E13 * T^{4} // this should be plus, not minus 
The 2011 code does not actually contain Wexler's over ice formulation, just a reference to it and an incorrect over water formulation.
Nielsen Murphy Vömel Alduchov 96 29.32707 24.7219 24.721994 24.72219 over ice coefficient 
Nielsen 29.32707  ln(100) = 24.7218998 => 24.7219 
But where did the extra Vömel digits come form?
Assuming that he copied the over water function and just typed new coefficients (something many of us do), he might not have noticed that the over ice value has only 4 digits after the decimal and that the over water value has more.
Vömel 16.635794 over water 24.721994 over ice 
So, How big an error is this?
Sonntag fix  change is not significant °C old new 30 0.38003 0.37999 10 2.59917 2.59893 
This is my primary source for the following
The vapour pressure of both ice and liquid water at the triple point is
P_{t} = 611.657 ± 0.01 Pa at temperature T_{t} = 273.16 K (Guildner et al. 1976, Vapor pressure of water at its triple point. J. Res. Natl. Bur. Stand., 80A, 505–521) 
There are 3 Goff and Gratch equations  1946, 1957, 1965.
Algorithm  Murphy and Koop  Vömel  
Goff and Gratch 1946 over water  log (101325)  log (1013.246)  5.005716612414
3.005714897949 
Goff 1957 over water WMO_Goff  log(611.14) 2.78614071  0.78614  Close enough 
Goff 1957 over ice WMO_Goff  log(611.14) 3.566506  0.78614 3.56654  2 constants are different 
Appendix C contains a table with the expected saturation vapor pressure values both over ice and over water  the intended purpose is to check computer code. Those values (specified with 4 to 6 significant digits) agree with the values computed by my software when rounded to the same precision. Note that the values in the table are specified in Pa and my software produces results in hPa (mbar)  the difference being 100 (10^2).
The following formulations are in Appendix A, including a few not found in other sources.
The saturation vapor pressure over ice depends on the crystallization  hexagonal, cubic (below 200K), amorphous (below 160K). (Once, when cleaning a home freezer, I saw what appeared to be cubic ice on some old ice cream  about 20°F (244K). Before that, I had no idea such a thing was possible.)
A paper presented at the EUROMET 2004 Workshop on Uncertainty in Humidity Measurements. 22th February 2004, EUROMET THERM Technical Committee Meeting.
As the name suggests  this paper is primarily focused on uncertainty in the calibration of humidity sensors.
This discusses the Wexler formulation and provides a table of coefficients. In particular, the Sonntag (1990) coefficients fit the Wexler formulation to ITS90.
The following table compares the coefficients in this paper to those in the Vömel paper. The first conversion is easy  Nielsen provides results in Pa, Vömel uses hPa  a difference of 100. However, the comparison is difficult because they don't appear to use the same versions of each algorithm. For instance, Nielsen provides coefficients for Sonntag (1990) and Vömel uses Sonntag (1994). Over both water and ice, these two have identical coefficients except for the scale factor. As shown in the table below, the coefficients are (nearly) equivalent to the scale factor of 100 .. except that one of them does not have enough significant figures. Unfortunately, since I do not have access to the original Sonntag papers  they are about $33 each to read!  I don't know which source is wrong.
The 4 Wexler papers are a bigger problem.
I only compared the following algorithms (coefficients in Table 12, p 24)
Algorithm  Nielsen  Vömel 2011  

Over water  Wexler (1976)  Wexler (1977)  The coefficients are identical except for the sign of the T^4 term
+/ 4.4412543E13 * T_K^4 =0.003597416 when T_K = 300 Vömel fixed this in 2014 and now they are identical 
Over ice  Wexler (1977)  HylandWexler (1983)  These have identical coefficients
Note: these are not the same as the Wexler 77 coefficients over ice 
Over water  Sonntag (1990)  Sonntag (1994)  scale factor  21.2409642 vs 16.635794
exp(21.2409642  16.635794) = 100 The other 4 coefficients are identical 
Over ice  Sonntag (1990)  Sonntag (1994)  scale factor  29.32707 vs 24.721994
exp(29.32707  24.721994) = 99.99058184 The other 4 coefficients are identical 
ln(100)  4.605170186  Computed via Excel 
21.2409642  16.635794  4.605170200  Very close 
29.32707  24.721994  4.605076000  This is the problem 
At any rate, I used the opportunity to look at the science behind their model. The two saturation vapor pressure formulations (one equation, but with different parameters over water and over ice) are implemented in the QSAT function in UTILDBL.f. I was surprised to see that it had a different form than any of the Vömel equations. I eventually learned that they are using the highly inaccurate August equation, but with different parameters. It turns out that over the range of atmospheric temperatures, their formulation is probably accurate enough.
About 6% error at 40°C (40°F) About 4% error at 40°C (104°F) < 0.06% error at 6°C ( 44°F) 6.108 mBar @ 0.01°C 
Atmospheric Noise Temperature Induced by Clouds and Other Weather Phenomena at SHF Band (145 GHz)
Christian Ho, Stephen Slobin, and Kelly Gritton, August 11, 2005 
I discuss this reference in detail. On page 18, they provide a number of saturation vapor pressures, but provide no reference on where they come from (or how they were computed). Since the pressures are provided with 2 decimal places, I assume that the temperatures given are exact and not rounded from something close. While their values don't exactly match any of the formulas in my software, they almost match WMO_Goff.
Table 5 provides
Water Vapor  Attenuation scale height = 2.0 km 
Oxygen  Attenuation scale height = 5.4 km 
Cloud  base = 1 km top = 3 km 2 km thick 
A surface water vapor density (absolute humidity  AH) of about 7.7 g/m3 "results from a surface temperature of 15 C and a relative humidity of about 58%".
Table I in the typed (1997) version (not in the 1996 paper) appears to be wrong. I created a calculator to perform the computations and got significantly different answers.
1. Introduction (paragraph 3) The most precise formulation of vapor pressure over a plane surface of water was given by Wexler (1976). The relative errors of Tetens' (1930) formula and one due to Buck (1981) (...) are shown in Table I. Table I. Relative errors(%) of Buck's (BU81) and Tetens' (TE30) approximations. 


To use the calculator,
Nielsen 29.32707  ln(100) = 24.7218998 => 24.7219 Murphy Vömel Alduchov 96 24.7219 24.721994 24.72219 over ice coefficient 
By inspection, it appears to me that both Vömel and Alduchov contain a typo.
°C Table 2 Calculator 80 47375.85 47374.847 
Atmospheric Chemistry and Physics by Seinfeld and Pandis (2006) 
This formulation is identical to the 1971 Richards formulation with the exception that Richards used 373.16 K (vs 373.15 K) as the calibration point. Lowe77 eq7
Basically, there are several definitions of the metric temperature scale and various algorithms (formulations) use one standard or another.
Of course, this makes it very difficult to analyze atmospheric data over a large interval  the standards changed, so the measured values changed. However, it is hard to find the correct metadata to make the necessary adjustments.
The International Temperature Scales  1878 to 2000
The International Temperature Scale of 1990 (ITS90)
International Practical Temperature Scale of 1968 (IPTS68)
Guide to the Realization of the ITS90
Most of the information on the Antoine and August equations comes from here. Not because there aren't other sources, but just because those sources are not available online.