Bally boards were the best to work on when they were used on route during their intended commercial service life. The holes between board sides/pads are indeed plated. A board exposed to leaking batteries, especially in storage without the game being turned on daily to dissipate moisture can easily be to blame what you're seeing.
Williams boards, made by the former Menasha Controls Corporation were a couple steps below Bally's stuff in terms of quality, durability and serviceability.
Like Pinfixer said above, A high quality desoldering station is by far the best way to repair these boards. Most components fall off of the board when the last pin is desoldered.
All of the distributors of commercial coin-op equipment had them (I worked briefly for Bally Midwest-the former Empire Distributing) which had two of the Pace setups. As soon as I started working for a route operator in 1979, I convinced them to invest in a Pace system and lots of spare tips, Glass tubes, cleaning brushes both types of filter pads as well as improved test equipment.