1) МЫ шли по парку.( в одную сторону шли? Разница только в стороне?) There is action at point of the past time here. It can be better translated as "We were walking through the park" (at the moment in past)
2) Мы ходили по парку. There is action in indefinite period of the past time. Here could be better "We walked in the park" (sometimes walked, we don't know when, how longtime)