The buildings systems (HVAC, Elevator, Sprinkler, Electrical) are the main concerns for older properties. You should ensure that they are not only operational, but in today's energy efficient world know how antiquated they are compared to other newer'ish buildings, and what the cost is to upgrade or replace these systems.
How are the common areas? Dated, adequate, renovated, a shambles? These are all areas that may need to be upgraded to attract new tenants into the building. Does the building compete with other newer multistory office buildings for tenants?
When it comes to older office, in particular multistory office buildings, the challenge is often looking beyond 'it pays a decent return' and digging in to understand what is required to day to keep vacancies low, and equally or more importantly what will be required tomorrow to attract or keep tenants?
One thought, I've been involved in an older office building, a mid sixties building, and the lobby (renovated) and common areas needed to be addressed, at least for budgeting. In addition, the individual offices were of the old style were the office walls were something of a flimsy somewhat portable walls. To combat this, and also upgrade systems as larger vacancies occurred the ceilings were removed, the HVAC ducting removed, the concrete was stripped via a sandblast, and then attractive and exposed HVAC ducting was installed. The office walls were demoed, and conference room(s) constructed.
With the flimsy walls removed the offices have an open space plan, and with the ceilings exposed the renovated offices emulate a loft space. Not only was the creative renovation cost effective but higher rents were achievable for more desirable office space.