I heard quite a few. Again I stress that I am not taking sides here or saying I fully agree with every point, just giving some examples of reasonable arguments for balance since arguments the other way have been widely discussed anyway.
The EU has a democratic deficit. It is a legislative and executive body where those with the most power are selected so indirectly that they have little personal accountability. Many EU Commissioners are career politicians who have become unpopular in their home state and have been given the job as a golden ticket.
The EU is systemically flawed as a financial arrangement. It has a currency union but only limited tax coordination and this will inevitably lead to internal conflicts during times of economic pressure such as the Greek situation.
The EU is a protectionist trade bloc. In the short term, this means membership is good for free trade within the bloc but bad for trade across its border. An example is that there is fresh produce we can source from either EU or African suppliers but the latter are artificially expensive if we have to impose the common tariffs, which reduces competition and so harms our consumers. The UK has been increasing its international trade for a long time but the EU has represented a decreasing proportion of that trade as a long term trend even with the bias that membership creates, so remaining in the bloc is the wrong side of the line to be on in the long term.
The EU does not have a good track record of negotiating international deals on behalf of its members. It has so far failed to establish comprehensive FTAs with many of the largest economies outside its own members and while its size is an advantage in negotiations, it also has to reconcile the sometimes contradictory interests of its many members, which can cause problems as illustrated by the CETA process.
The EU is bureaucratic and slow, and its philosophy of trying to unify everything creates many bad regulations and interferes with free market economics in ways that can be detrimental to members. Its handling of VAT and many digital/technology issues are recurring examples where it may do more harm than good to some member states or their people or businesses.
The EU has an expansionist agenda whether openly acknowledged or not. It has seen considerable scope creep since the last popular vote to stay in and it has a track record of trying to bypass popular consent or seeking that consent repeatedly until it gets the answer it wants, so not leaving now also leaves us committed to an uncertain future.