(Cross posted from Super User per suggestion there)

At the office, I have inherited a network that I am still trying to fully comprehend. I have a problem today with a new connection between:

• A port on a Cisco Catalyst 3750 [WS-C3750G-48TS-S running C3750-IPSERVICESK9-M version 12.2(53)SE1]
• A port on a Cisco ASA 5505 [ASA Software version 8.3(2)]

The 3750 is home to a Vlan that has a few ports assigned to it.

interface Vlan3
 description Internal network (172.18.160.0/24)
 ip address 172.18.160.1 255.255.255.0

I have a host (outside of my control) that needs to be in this VLAN (i.e it must have an address 172.18.160.something/24) that also needs to access the Internet.

To accomplish this, I ran a link from the Catalyst (Gi1/0/13) to the ASA (Ethernet 0/5). I configured the Catalyst port like so:

interface GigabitEthernet1/0/13
 description To ASA, 172.18.160.69
 switchport access vlan 3
 switchport mode access
 speed 100
 duplex full

I configured the ASA like so:

interface Vlan1
 nameif inside
 security-level 100
 ip address 172.18.160.69 255.255.255.0

interface Ethernet0/5
 speed 100
 duplex full

Then I plugged the host into Ethernet 0/4 on the ASA and instructed its owner to make its default gateway 172.18.160.69. I made a NAT rule in the ASA and set up some rules, and it's able to access the Internet without issue.

However, I noticed that the Catalyst reports a ton of packets being dropped toward the ASA.

Catalyst3750#show interfaces GigabitEthernet 1/0/13 | include counters|drops
  Last clearing of "show interface" counters 00:28:13
  Input queue: 0/75/0/0 (size/max/drops/flushes); Total output drops: 136909347

This is a huge number of drops, since there's not much traffic on this VLAN at all.

I tried these things:

• Make sure speed and duplex agree on both sides (100 Mbps / Full)
• Set no cdp enable on the Catalyst Gi10/13
• Set no keepalive on the Catalyst Gi10/13
• Checked for excessive CPU usage on both
• Checked for excessive traffic on both

Am I missing something? Any help would be appreciated.