The overall organization of EUs legislative institutions is the European Commission which is a supposed to be a nationally independent and politically neutral organ with a primary task of proposing legislation, the European Parliament, supposed to be the voice of the people and the Councils who represent the national governments.
Apart from the political institutions there are the judiciary systems of Court of Justice, General Court and Civil Service Tribunal. Court of Justice has a focus on taking requests on matters where EU legislation might be in conflict with national law and appeals from the General Court. The General Court handles proceeding involving EU institutions and legal European personalities (yes, EU institutions, governments and companies are legal personalities!) as well as several more specific types of cases. It also act as an appeal court for the Civil Service Tribunal.
The Civil Service Tribunal is handling legal actions from EU personnel against EU institutions.
The judiciary system has occationally been asked for opinions on proposed legislation.
Two other institutions are reviewing legislation and giving opinions on the commissions work. The European Economic and Social committee (EESC) consists of 334 members of which 114 are employers, 117 worker organizations and 104 various interests including handicap organizations, environmental, research etc. They are nominated by national governments, but act independently and presumably without national bias. EESC works as a “bridge between... EU institutions and EU citizens, promoting a more participatory, more inclusive and therefore more democratic society in the European Union”. Yeah... Apart from the shameless self-marketing, the job is to assist the legislative institutions in forming opinions on legislative matters. These handpicked lobbyists are there to influence politicians in the legislative process and to form common opinions on the proposed legislation.
The other review group is the Committee of the Regions. They are political representatives of regional and local governments in EU member states and represent the local opinions on proposed legislation. The members are part of one of five political groups: European People's Party (conservative, EU positive), European Conservative and Reformists (conservative, EU skeptics), Alliance of Liberals and Democrats for Europe (liberals, EU positive), Party of European Socialists (socialist, EU positive) and European Alliance (local parties primarily. It is the only group with no direct EP equivalent).
There are several specific institutions for protection against misuse. The European Data Protection Supervisor, who ensures protection of privacy for European citizens in EU institutions. The Court of Auditors audit the use of funds in EU to protect against fraud. The Ombudsman which is somewhat of an administrative auditor of EU institutions, by public requests. Unfortunately he is elected by a such institution, namely the European Parliament and his action is limited to negotiating a better solution and if that fails, writing special reports to the parliament! He has no permission to investigate national parliaments or the judicial wing of EU.
ECB is the central bank of the EURO-countries. It acts as more or less a national bank in the EURO-zone.
Apart from those there is an investment bank and several other EU institutions like Euratom, EUROPOL and scientific, legal or political support facilities across Europe. About 40 such specialised agencies and decentralised bodies exist in total at the moment.
Sources:
http://www.eca.europa.eu/en/Pages/ECAWork.aspx
http://curia.europa.eu/jcms/jcms/T5_5230/
http://www.eesc.europa.eu/resources/toolip/img/2013/04/19/organigrammepolitic_2013--2.jpg
http://cor.europa.eu/en/about/Pages/political-groups.aspx