Examining animals, on a farm level can be tricky. Records are very helpful. My professor in zootechnics says that the Japanese are the best record keepers. They keep a record of all the events in the farm in a very systematic way. He narrates that even after decades, their farm records are still available. Of course these old notes are important because production events and even production problems come in a cyclic manner. So all the events experienced in a farm, even if the personnel has been changed, can be quickly read.
All the important data are recorded: feed consumption, growth, weight, mortalities, morbidities, reproductive parameters... In short, everything must be recorded, even changes in weather patterns or temperature fluctuations must be written. Some farm owners neglect these basics. Most are only after the financial records.
For me, even a very simple recording system would do because I can easily compute for the secondary parameters as long as it's accessible and is systematically done.
----
I was also earlier thinking of examination of animals in the farm. The best way for me, is to "feel" them. One must be on the level of the animals to properly assess what and how they feel. For example, feeling the air inside a broiler brooding area is useless. In Physics, warm air rises, so expectedly, the air inside would be warm. But to get an idea of what the chicks feel, try to touch the litter. The chicks are standing and roaming on the litter materials and not flying in the air (of course!) so the quality of the litter is important.
Use your other senses too. How do they sound? How do they smell? How do they behave? These must all be noted because in a way or another these will have an effect on their short lives.