My Alarm Bells were going off in my head because I knew that wasn't one of the legal fixes but I let him explain the situation to her.

From what I can tell from BP, after careful screening tenants, having consist tenants doesn't seem to an alarming issue. 

Would installing an alarm system help with the insurance cost being that the property is vacant, or should I just avoid that expense?  

@Adam Moehn If you actually started April 1st, I wouldn't be as alarmed, but still double check if your rent is appropriate.Two tips I give to beginning landlords.#1 When someone comes to view it, before the showing I say something like "Quick market research question for you - when you look for an apartment what sources do you use."

Due to how old our homes are in this area we see a good amount of this because that is how they built homes back then and from my experience they are nothing to be alarmed with, I happen to like them better unless there are flaws that are very easy to see.You can check out my post on this forum explaining some of the issues and differences about the foundations, I am not an expert but I know a good amount about them because I must be able to point out to my clients when their might be an issue with a property.https://www.biggerpockets.com/forums/16/topics/148599-how-old-is-too-old?

Alarm installation - generally done when folks are home.Garage Door installationReal Estate Agent - everyone looks after work or one weekend for the most part.  

I'm not sure I'd be alarmed, but certainly the title company and/or selling attorney can clarify.

We always check smoke alarm batteries and filters, and one of our longer-term tenants now actually leaves post-it notes around the place saying, loose closet door, or wobbly fan, and we fix anything minor that we can take care of while there.  

Although the fire department does the inspection at sale it is good to have your inspector know if what you have in terms of alarms, emergency lights or sprinklers will pass that inspection.

If it's increasing, then that is a cause for alarm.