I've set verify = header_syntax in my ACL, but this causes Exim to complain about header lines like To: Work: Jim <jims@email>, Home: Bob <bobs@email> which look all right to me. Is this a bug?

No. Header lines such as From:, To:, etc., which contain addresses, are structured, and have to be in a specific format which is defined in RFC 2822. Unquoted colons are not allowed in the phrase > part of an email address (they are OK in other headers such as

Subject:). The correct form for that header is

To: "Work: Jim" <jims@email>, "Home: Bob" <bobs@email>

You will sometimes see unquoted colons in To: and Cc: headers, but only in connection with name lists (called groups ), for example:

To: My friends: X <[email protected]>, Y <[email protected]>;,
    My enemies: A <[email protected]>, B <[email protected]>;

Each list must be terminated by a semicolon, as shown.