As far as I can tell, both окидывать взглядом and заглядывать have the same general meaning. Are there any nuances that they don't share? Is one more colloquial?
I think they don't have the same general meaning. "Заглядывать-заглянуть + Accusative (куда?)" means "to peep in", "to look into", "to have a look at" or "to drop in", "to call in". So, normally this verb means "to look inside smth" or "to come, enter somewhere":
Я заглянул в книгу. I looked into the book.
Она часто заглядывала к нам. She used to call in to our place often.
"Окидывать-окинуть взглядом + Accusative (кого? что?)" means "to glance over", "to rake". It has the meaning of looking attentively and having a wide space to look at.
Профессор окинул взглядом всю аудиторию. The professor glanced over the whole audience.
As you can also see, "заглядывать-заглянуть" is always used with a preposition, while "окидывать-окинуть взглядом" is used with a direct object.
"Окидывать-окинуть взглядом" is a synonym of "оглядывать-оглянуть + Accusative (кого? что?)" which also means "to take a view of", "to look over (round)", but has a nuance in the meaning because it can also be "to examine":
Профессор оглянул всю аудиторию. The professor looked over the whole audience.
Что ты меня оглядываешь? Why are you examining me?
I would like to add a few meanings and use cases of
"Заглядывать вперёд" means "to look forward", but it can not be as "
оглядывать вперёд", it's incorrect. However it is possible (and widely used) to say:
"Оглядываться назад"(1) means "To look back", e.g. when someone's walking or in terms of passed days, or time that has gone (look back into the history) but can not be "
оглядывать назад", it's incorrect. However it is possible (and widely used) to say:
"Заглядывать назад" means also "To look back" is also can be said in terms of passed days, or time that has gone, can not be said when someone's is walking, more likely wheh is not moving -sitting or standing.
"Он заглядывается на других девушек" means "He looks at other girls", it is possible to say "Он оглядывается на др девушек" but this means that "He turns his head around to watch other girls(when passing by them)"
"Заглядывать в душу" means "To look into the soul" but it can not be as "
(1)"я оглянулся посмотреть не оглянулась ли она чтоб посмотреть не оглянулся ли я" words from a famous song, means "I looked around to see if she did not look back to see if I did not look back"