Agree with just generally being organized, knowing the anti-platelets and anti-coagulants, etc. If you know CEAP criteria and don't know some of this basic stuff, I frankly would think you were super book smart and clinically useless, but that's just me. Focus on understanding urgent and emergent things. You have time to look up info on optimal dialysis access if you're consulted for access placement, or carotid stenosis duplex criteria, but other things are more urgent and you want to quickly be able to know what to look for and make a complete assessment. The above is great, but there are a few much more high yield things that I wish my interns knew in the middle of the night that haven't been mentioned:
Understand acute limb ischemia. There is a rutherford classification for this. You will never be the one making the call regarding if the patient needs the OR emergently or the next morning, but knowing the components of that and being able to tell your fellow when you present the patient to them is very important (are they experiencing paresthesias, motor deficiency, or pain only, and what is the duration since symptom onset).
Know if the patient has a contrast allergy. Many patients will require either a CTA or formal angiography and this can mess up the OR schedule if they aren't prepped.
When you're consulted for a wound, in general assess for an arterial or venous component to their pathology. (See pulse exam above. Probably most important thing mentioned). Some wounds are simply secondary to diabetic neuropathy, but others need revascularization prior to amp, and still others are venous and simply need some good compression, elevation, and wound care.
Understand spinal drains. I expect the intern to call me if/when changes to this need to be made, BUT I have had situations where there is a problem with the drain that has gone unnoticed for several hours, so it's critical to have a basic understanding of them. Every institution is different in how they manage them, so I won't go through details here. Also generally understand there is a risk for spinal cord ischemia in patients who have undergone major aortic operations (generally seen with extensive TEVAR coverage or complex endo repairs involving longer lengths of aorta), so if a patient has leg weakness after one of those, even days later, don't mess around with that. Tell someone right away, and know your institution's rescue protocol.
If something is bleeding, don't panic. Place your finger on it. Take a deep breath. Call for help.
Finally, if you want a nice pocket reference manual, stop by a case with a Gore rep and ask if they can get you a copy of the Combat Manual. They will give it to you for free, and it is intended to cover the most commonly encountered scenarios in vascular surgery. I wish I had it as an intern. It is about a decade old now, but it's still pretty relevant.