Hello Trevor,

this is what I got with M10.1.0 after adding "PlotRange -> All" to your code. It seems to work up to expectations.

In[1]:= Needs["ErrorBarPlots`"]

ErrorListPlot[{
  {
   {{0.3, 0.2}, ErrorBar[0.14, 0.1]}, {{0.05, 0.86}, 
    ErrorBar[0.01, 0.2]}
   },
  {
   {{0.7, 0.024}, ErrorBar[0.14, 0.005]}, {{0.48, 0.15}, 
    ErrorBar[0.13, 0.041]}
   },
  {
   {{0.65, 0.0007}, ErrorBar[0.2, 0.0002]}, {{0.34, 0.25}, 
    ErrorBar[0.18, 0.13]}
   }
  },
 Joined -> True, Mesh -> All, PlotMarkers -> {Automatic, Medium}, 
 PlotStyle -> {Blue, Red, Darker[Green]}, PlotRange -> All
 ]