Many mild or asymptomatic cases definitely go unnoticed and the actual number of infected could be a few times higher but essentially they aren't the main problem (especially under a lockdown) - the biggest issue are those that require medical attention and hospitalisation as that's what makes the healthcare system break so as long as the testing levels stay approximately the same it is still a good enough stat to evaluate the general trend. What's encouraging in Italy's case is that they're carrying out more tests every day and the number of new cases still seems to be stable (in fact a somewhat larger increase in daily cases a few days ago was attributed to adding the backlog into the total count) - also the number of new cases in ICU seems to have stabilised at around 100 per day too. Those two are the main factors that make me cautiously optimistic - but it's definitely too early to tell. The situation seems to be slowly stabilising and improving in Lombardy only though so it's quite likely that the numbers will shoot up again as South Italy (with much worse standard of medical care) reaches the peak.
As for trusting the numbers to be accurate; that's always a difficult one... You can only work with and make your observations from what you're given by the authorities. A lot depends on the way the cases are counted and the way those numbers are then reported so you're definitely right that it can be misleading. Even the number of deaths in Italy is a questionable one because of the way it's reported - it essentially shows the number of people who passed away WITH the virus - but that doesn't necessary mean that the virus was the cause of death. In other words, you could die of an unrelated chronic (or accute) disease and have no or just mild symptoms of Covid-19 but if you test positive, you are automatically included in the total count of the virus fatalities.