Is it true that small firms can discover the abilities of their workers more quickly than large ones because they can observe the workers more closely at a variety of tasks"
This is a great question. I would agree generally speaking (as long as the company is good). I say "generally speaking," because some small firms are a mess and they do not help anyone. Furthermore, smaller companies may be busier and so may not have the resources to help all that much.
With this stated, smaller firms may have several advantages. First, since they are smaller, everyone knows everyone else or there is a better chance for this to take place. For this reason, people know your level of skill and if the firm is a good one, they can help you find your niche and develop your skills.
Second, smaller firms are more apt to treat people as individuals. In other words, there is more personal attention. This can help tremendously in career development.