Most other Shippers don't agree that Dawn's feelings towards Paul are important. In fact, out of all main and secondary characters, she is the only one who really shows any interest in Paul, or even in his skills.

"Different Strokes for Different Blokes!"

Dawn admired Paul when he easily captured an Ursaring, although he didn't return her sentiments.

"A Gruff Act to Follow!"
When Paul stared at Dawn after she stopped the argument, she worriedly asked what's wrong.
Dawn tried to stop the argument between Paul and Ash. However, she became very furious about the fact that Paul didn't remember her at all.

Dawn blushing and smiling at Paul when he stands up to leave during Ash's battle Dawn is the first to notice it.

"Top-Down Training!"

When Paul says Torterra is his first Pokémon, Dawn appears impressed.

"Riding the Winds of Change!"
When Paul leaves the town with Gliscor, Dawn just slightly smiles after him.

"Glory Blaze!"
Dawn steps in while Ash and Paul are arguing, continuing in Ash's place.

"Chim-Charred!"
As the episode closes, Dawn is seen standing separately from the rest of the group, gazing after Paul as he leaves; in some IkariShippers' opinions, this is a slightly infatuated look in her eyes.

"Aiding the Enemy!"
Dawn comments several times on Paul's actions showing that she isn't indifferent to him. She also seems annoyed by his cold attitute towards her and her friends as she says "Man, what's his problem?" and "What's wrong with you Paul?" when he leaves ignoring them.

"A Pyramiding Rage!"
When Zoey points her finger menacingly at Paul, Dawn holds her back to stop the upcoming argument. As Paul leaves, Zoey says she hopes Candice will defeat him with Dawn having a very worried look on her face.

"Familiarity Breeds Strategy!"
When Paul is talking to his brother, Dawn is seen eavesdropping. When Paul discovers her, she follows him outside and they start talking. Paul appears to be opening up to Dawn and tells her why he doesn't like Ash. Later when Ash and the others appear, Dawn stands quietly beside Paul, but then quickly runs over to Ash's side and gives Paul a smile and slightly blushes. It seems like she understands Paul now, and later she says she doesn't know who to cheer for.