Does a blanket UCC on Inventory take precident over taking a UCC on a specific unit? e.g. If another bank has all inventory and I want to take a specific piece of inventory and list serial number and description, would our bank have a first lien on the specific unit

It goes by the order of filing so a blanket on equipment filed first would take priority over your specific filing unless you can prove you have a purchase price security interest. This can be tricky to prove but doable. Another option would be to get a subordination agreement on the specific piece of equipment you want your security interest in from the bank who has the first blanket filing.

I would suggest you look under the UCC (Article 9) for purchase money security interest. There is a seperate section or sub section which talks about the requirements for this. If you meet them all then you can take an interest in a specific unit and have priority over a blanket interest.

ahb is correct. Specifically look toward 9-312(3):

(3) A perfected purchase money security interest in inventory has priority over a conflicting security interest in the same inventory and also has priority in identifiable cash proceeds received on or before the delivery of the inventory to a buyer if:

(a) the purchase money security interest is perfected at the time the debtor receives possession of the inventory; and
(b) the purchase money secured party gives notification in writing to the holder of the conflicting security interest if the holder had filed a financing statement covering the same types of inventory (i) before the date of the filing made by the purchase money secured party, or (ii) before the beginning of the 21 day period where the purchase money security interest is temporarily perfected without filing or possession (subsection (5) of Section 9-304); and
(c) the holder of the conflicting security interest receives the notification within five years before the debtor receives possession of the inventory; and
(d) the notification states that the person giving the notice has or expects to acquire a purchase money security interest in inventory of the debtor, describing such inventory by item or type.

You should consult a qualfied attorney to help you establish your procedures and notification requirements, but it is a common practice and can be done successfully.