Well, if we provide confidence intervals it should provide some kind of "safety"... but even so, with forecasting the only assurance you can get is by testing it against known historical values and checking it's accuracy (and even that way, historical results are no guarantee of future performance).

What kind of details would you say can be inspected to see if the model is reliable? AR or MA orders, inferred seasonalities? They can give me some notion of what kinds of assumptions were created about my data, but do not guarantee that it will perform :/

For instances where that kind of insight is needed, I don't think our way is the way to go, but rather the use of some forecasting package (R's Forecast or FB's Prophet) and a more exploratory work. But we're looking more at instances where what matters are the forecasted values and not so much the information underneath - automated anomaly detection systems, consumer-facing apps, and along those lines.