Despite being an Enhanced Original Vampire in The Vampire Diaries, Alaric Saltzman wasn’t immune to vervain, which was a major plot hole in the show. Alaric Saltzman (Matt Davis) is introduced as the history teacher at the high school, while in reality, he was hunting vampires to avenge his wife’s death in the first half of season 1 of The Vampire Diaries. After becoming closer to Elena and Damon, he’s turned into a vampire himself by Esther at the end of season 3. At first, he was turned into an Enhanced Original Vampire as Esther did an immortality spell on him after changing him. This spell tied his life to Elena, meaning the only way to kill him was to kill her. The spell made him immune to threats that harm other vampires.
Vervain is the vampires’ best-known weakness; the only vampire who had immunity was Katherine, played by Nina Dobrev. If a vampire comes into with vervain, it causes immense burns, and if vervain is eaten, their throat will be burned, and they’ll become sick and weak. The herb, of fluctuating availability in Mystic Falls, can also be used to protect humans against vampire compulsion, as it won’t work if they have the herb on them. This weakness exists because when Esther used the immortality spell, she disrupted the laws of Nature. In order to balance them again, Nature gave vampires various weaknesses, including vervain.
Since Alaric became an Enhanced Original Vampire not directly from the white oak tree, logically vervain shouldn’t harm him, in the same way white oak daggers can't kill him. However, in season 3, Alaric ingests vervain and is affected by it similarly to other vampires. This is a major plot hole, as the only thing that should be able to kill him is Elena Gilbert’s death. This weakness is never explained through the rest of the series - it’s just accepted that he’s also affected by vervain, like any other regular vampire, despite his beginnings.
There have been possible explanations online, though nothing was confirmed by the show. Some have speculated that Esther stilled derived Alaric’s power from the one true source of power, the white oak tree, and the only difference was that she tied his life to Elena’s life. She still followed the same ritual when turning anyone else into a vampire, so it's unsurprising that he would react to vampire's weaknesses the same way. Since all vampires have their power derived from the white oak tree, there couldn't be a vampire that is immune to vervain. However, this explanation doesn't explain how Alaric, one of the most important characters, is immune to weapons made from the white oak tree directly.
Others have said that Maria Howell's Ayana's warning that the Spirits would turn on the Original Vampires applies to Alaric too. The Spirits are the extremely powerful collective of non-living witches on "The Other Side". Ayana warned Esther that using the immortality spell to protect her children will cause the Spirits who supplied them with their magical knowledge to turn on them. It would be using the magic they were given to disrupt the laws of Nature, which would anger The Spirits. Later, it's mentioned that the Spirits turned on them to make vervain burn them by Claire Holt's Rebekah. It’s possible the same Spirits turned on Alaric, since he was turned into a vampire using the same spell. Unfortunately, without confirmation from The Vampire Diaries, this detail still appears to many like merely a glaring plot hole.