I read the reviews here before visiting, both the good and the bad, and the simple truth in my mind is that they are all correct!
This place DOES feel at times like it is falling apart. It is grimy, there is bird crap covering some of the outdoor staircases, some of the shared bathrooms are dingy, and they charge hourly for wi-fi...
BUT... yeah the place has character, but it more than that. People do come back here time and again. The social vibe of the place is great, mixing such experienced returnees with newbies.
Chennai was my very first experience of India. Broadlands was not the luxurious comfortable splurge that many friends suggested would be the best way to ease myself into the country. But with pleasant courtyards, a higgledy piggledy layout with staircases and alcoves everywhere (meaning you feel like you just have to explore) and a spartan but sunny roof area overlooking the nearby Mosque, it did the trick.
Broadlands does feel like a traveler oasis within the city. It may be showing its age, but there is something about the place that grabbed me and made me feel most comfortable. It is far from the best guesthouse / hotel I have seen in India so far (I have been in the country a month now), but if I was ever to return to Chennai I cannot imagine staying anywhere else.