What problems faced the new Stuart monarchy upon the accession of James I in 1603?

If we were looking at this as if it were an exam question we'd try to address maybe three areas that we could identify and talk about in some detail during the timed essay. Perhaps first we'd consider the persistence of religious conflict. The fracturing of the Elizabethan religious settlement after 1559 and the challenge faced by the emergence of Puritanism, as well as an ongoing Catholic threat. In relation to this latter point we might talk about the Gunpowder Plot and threats to the monarchy posed by various plots to kill the king. Then we'd look to address the fact of James I's Scottish kingdom and the attempts of later Stuarts to bring Ireland under Stuart rule. The problems of Stuart multiple monarchy can best be explored through the coronation ceremonies of both monarchs and the prevalence of Scottish noblemen at the English court. Equally given unique nature of the Scottish Reformation at the resultant Presbyterian Kirk this point could in more sophisticated answers be linked to the fact of religious differences. For a final paragraph in an exam answer we might look also to the personality of James I, the character of his court and specifically his relationship with his close and hated adviser, George Villiers, Duke of Buckingham. Specifically in keeping close to the wording of this question we might look to compare it to the nature of Elizabeth's reign and just how popular she had been as the 'Virgin Queen' before her death.