The ability to speak to random entities does not give you control or even rapport with them.
Make the druid do the legwork of earning the creature's trust and friendship. Don't let them automatically gain minions just because they picked this or that class. Would a bard become instantly able to ask NPCs for favors upon arriving at a new village? Probably not, and so shouldn't the druid.
Then, the animal has its own agenda. Pets like their owners and most of them are naturally as loyal as any tyrant would wish their henchmen to be. Wild animals are 80% focused on their own survival and 17% focused on the survival of their offspring (the remaining 3% is the influence of the chaos gods).
Next, beasts are not people. They don't think like people, they don't remember stuff like people. They don't pay attention to people like people, and they don't understand people's languages.
A rat may spy on a pair of rogues doing shady business, but its report of what happened should not include any details a sapient, language-wielding being would notice. What the rat might notice, remember, and report is left as an exercise for the reader.
Key wording from the spell:
The knowledge and awareness of many beasts is limited by their intelligence
Don't be afraid to roleplay the beast like an idiot savant. Force the player to spend time and resources training their would-be minions. The rat spying on the rogues might not even notice that money was exchanged. If the druid wants the rat to recognize gold coins, the rat needs to learn what a gold coin is and pick it apart from the other types. And I doubt a rat would be able to count more than two or three.
There might be some pressure to treat these animal NPCs as a mage would its familiar. They are completely different entity types, though.
If the player attempts to abuse the use of animals as an information gathering network, remember that the beast's life is a short one and fraught with perils. The rat spy might have a deadly encounter with Mr. Mittens, the miller's prized granary guardian and never be heard of again. Likewise, a bird messenger might unwittingly enroll in a tactical air superiority class taught by a hawk at the cost of a pound of flesh (and the bird weighed less than that, regrettably). This allows the DM to curtail any abuse and withhold information the DM doesn't want the players to have.
So, make the player work for the benefits they want, make sure they are limited, and don't be afraid of throwing Curveballs of Fate at their attempts. Just don't be an ass and turn this into a source of grief. Just challenge.
Ease is a close friend of boredom.