In the beginning of the game when Tricky and Fox first meet, Fox tells Tricky that his father had been captured. However, there was never any mention of his capture before this event, and when the Queen Earthwalker (Tricky's mother) tells Fox and Tricky about the King, there is noticeable surprise in their reactions.
When the first boss battle ends with the defeat of Galdon, he regurgitates Tricky, Fox, and the Spellstone. The problem here is that both times Galdon swallows Fox, Tricky is never taken with him.
After Fox and Falco defeats Andross, Falco's Arwing does not have any visible exhaust coming from it.
Kyte (The Pterosaur, or Cloudrunner) that is seen in the beginning with Krystal asks Fox if he is a friend of Krystal's. And Fox seems to know who he is talking about. Fox later addresses Andross's motives, referring to Krystal by name again. Fox was never given a chance to directly learn Krystal's name throughout the entire course of the game. Likewise, Neither should Peppy have known her name as he mentions a message he received from her. And Krystal also knows Fox by name, as shown in the message she sent (the one received by Peppy). In the beginning of Fox's part of the story, you can look at General Pepper's game status records, which names Krystal as being the one who released the first Krazoa spirit. Again, this is before Fox ever saw or heard about her.
There seems to be an inconsistency with the dinosaur language. Krystal is not a native to Dinosaur Planet, yet she seems to be fluent in the native language. When Fox first arrives, he relies on Slippy to translate until the translation machine is fixed. However, the Thorntail Hollow Shopkeeper seems to be able to speak English very well (because he is met before Slippy finishes the translator). When Fox first picks up the staff, the recorded message left by Krystal is in the dinosaur language, yet Fox seems to understand it despite needing all of the other conversations to be translated. After it has been activated, Fox and Tricky can hear Krystal's cries (possibly projected by Andross while he posed as a Krazoa spirit), and she is clearly speaking the Dinosaur tongue.