The instruction was that notes be taken on everything the babies did.
notes是名词!
be taking down=被记录下来, 是notes被记录下来, notes是有关婴儿的活动.
The instruction was that notes be taken on everything the babies did.
指导要求将婴儿们的一切活动都要记录下来.
instruction 后的从句中可以加should,也可以省略直接有动词原型,你所给的例子
属于后者!
The instruction was that notes (should) be taken on everything the babies did.