My usual recommendation when people are having problems with sketch patterns is to abandon them, create a single instance with the sketch, and then pattern that. I recommend the same here.
This looks like a bug in the user interface. At least in 2017... Might be fixed in 2018.
Here is a linear sketch pattern, spacing of 0.38mm:
Here's what happens when I type in 0.375 and hit "Enter"... You can see the preview in yellow of the closer spacing, but look at the spacing box... It's rounded to 0.38. At this point, if I hit the check mark or enter again, the preview and/or actual pattern instances move to a 0.38 spacing. The same sort of thing happens if I type in 1/16" and hit "Enter". The value in the box becomes 1.59mm instead of the correct value of 1.5875mm. If I hit the checkmark while the box still reads 1/16" the spacing is created correctly.
If I hit the checkmark immediately after typing 0.375 (instead of hitting "enter") the pattern spaces out correctly. I'm about 99.9% sure this is a bug, although a minor one with an easy workaround. The model posted has lots of other issues that I'm too lazy to fix, but the root cause of the original misalignment is the inappropriate rounding of the value typed into the "spacing" box. To fix, either type the value and immediately hit the checkmark, use the "dimension x spacing" and fix the dimension afterwards, or constrain the endpoints etc. in some other way after pattern creation as Dave mentioned. Again... It's a minor bug, but SW should NEVER round user input that generates geometry, no matter what the context.
Check your model units. Change them to the required precision.
I think SW is rounding it to the digits sets.