At least two candidates, including Ahmed Safadi, a major contender, were arrested for vote-buying the day before polling. They were released on bail.
Al-Assaf from the Islamic Action Front, Jordan's largest opposition group, said: "The parliament will be marked as a parliament that bought votes and spent time in jail. The people won't trust them.
"It's best to wait for a few days. We will see there was a lot of rigging of these elections."
The international observer missions say that the newly implemented election law is a big improvement on the past, but they say it should be seen only as the beginning of the reform process.
The law should be reviewed "to encourage political competition and the formation of coalitions and political parties," the National Democratic Institute said, as well as to bolster the legal framework around the formation of parliament.
Steps are also needed to ensure greater participation of women and young people and to develop the role of election officials, it said.
Wednesday's vote is the 17th time Jordan has gone to the polls to elect a parliament since becoming a nation in 1946, but it was the first time that an independent election commission oversaw polling.
A field of more than 1,400 candidates vied for the seats, of which 15 were reserved for women -- up from 12 in the previous parliament.
Jordanian Foreign Minister Nasser Judeh told CNN on election day that the vote was "the culmination of a constitutional process, the beginning of a new phase of reforms. It is a continuing process."
He said his country had "anticipated the Arab Spring," so the king began reforms "many years ago." But he acknowledged that protests in the region had expedited the changes inside Jordan.
The king has stated in discussion papers that the new prime minister will be designated based on consultations with the parliamentary bloc that has the majority, Prime Minister Abdullah Ensour said Wednesday.
The deliberate steps at transparency are crucial for a country that's under a great deal of political strain -- and whose stability has ramifications for the world outside its borders.
Recent events have threatened the fragile monarchy to the point that some analysts are warning of collapse.
What began with protests by the Islamic Action Front, Jordan's branch of the Muslim Brotherhood, has given way to broader unrest led by tribal factions known as al-Hirak ("The Movement").
Al-Hirak demands an end to corruption and calls for a new era of political reform in Jordan in which Islamists are almost sure to dominate.
In an effort to quell the protests, King Abdullah dissolved parliament last year and amended election laws.
In a region rocked by Arab Spring upheavals, Jordan has been relatively stable and is one of the few friends Israel has. It was against this backdrop that most Jordanians went to the polls.