"So I understand that if you apply an ACL to an interface then packets are inspected as they enter the switch."
Incorrect. The ACL applies to packets entering or leaving the VLAN interface, not a switch port's physical interface (for that VLAN).
"What is the behavior if you instead add that acl to a vlan and apply the vlan to an interface?"
Same as all other traffic on that VLAN. I.e. packets crossing the SVI are subject the ACL for ingress and/or egress.
"Is traffic being inspected everywhere that vlan is applied from multiple directions?"
Yes and no. Again, depends on whether traffic is entering or leaving a particular SVI. (Remember, as multiple switches can host the same VLAN, and if they are multiple L3 switches, you might have multiple SVIs on that VLAN. As ACLs are applied to particular SVIs, it's possible packets can be treated differently depending on which actual SVI they use. Further, the SVI doesn't have to be on the switch hosting VLAN ports, and even when SVI is on switch hosting that SVI's VLAN ports, those VLAN ports, on that switch, might not actually be using that switch's SVI for ingress and/or egress.)
NB: if the forgoing is unclear, ask further, as your understanding of SVI and VLANs might not be totally correct.
