other as pronoun

[licinio]

This book is no good, let's look at the other one.

If I said "at the other" without "one", would the sentence be correct and, if so, would the meaning change (still referring to an object)?

[Raymott]

This book is no good, let's look at the other one.

If I said "at the other" without "one", would the sentence be correct and, if so, would the meaning change (still referring to an object)?

Yes, you can say, "Let's look at the other", but it doesn't sound as natural. (It sounds like rather formal British to me). The meaning is the same, but it might not be as obvious to the listener. Even more obvious is "Let's look at the other book".

[SoothingDave]

If you omitted "one" it would still be understood to mean the same thing.

[bhaisahab]

I would be quite likely to say "let's look at the other" I don't find it particularly formal.