Red Flags for rental brokers/agents?

[Parney Willson]

I am working with a rental broker. The relationship started out fine, but then I asked to see an apartment that we already saw again to see what it is like during the weekend instead of the week. They said no because they "don't show listings twice. One time should be enough." 

Long story, short, after explaining a bit more why, they said okay as long as it is just the one I'm interested in and not all the ones we saw (which was what I wanted all along). However, when I tried to schedule they are suddenly unavailable the whole weekend and want me to wait until after the weekend.

I don't feel right about this, but not sure if it's just me being overly cynical or if this is a red flag and I should move on from this agent. I feel bad calling up the listing agent and applying with them. I can wait until after the weekend but something doesn't sit right with me and feel like the agent is just blowing me off vs simply being busy over the weekend.

Am I being too cynical? Also what are some other red flags to look for in a rental agent?