Estou achando que é um erro do Eclipse, pois tudo está funcionando perfeitamente apesar da mensagem.

Tem algum problema no meu projeto. Agora tentei injetar o EntityManager no ProdutoDao e o Toncat está dando esse erro:

GRAVE: Exception sending context initialized event to listener instance of class [org.jboss.weld.environment.servlet.Listener]
org.jboss.weld.exceptions.DeploymentException: WELD-001408: Unsatisfied dependencies for type EntityManager with qualifiers @Default
  at injection point [BackedAnnotatedParameter] Parameter 1 of [BackedAnnotatedConstructor] @Inject public br.com.caelum.vraptor.dao.ProdutoDao(EntityManager)
  at br.com.caelum.vraptor.dao.ProdutoDao.<init>(ProdutoDao.java:0)

    at org.jboss.weld.bootstrap.Validator.validateInjectionPointForDeploymentProblems(Validator.java:361)
    at org.jboss.weld.bootstrap.Validator.validateInjectionPoint(Validator.java:282)
    at org.jboss.weld.bootstrap.Validator.validateGeneralBean(Validator.java:133)
    at org.jboss.weld.bootstrap.Validator.validateRIBean(Validator.java:164)
    at org.jboss.weld.bootstrap.Validator.validateBean(Validator.java:507)
    at org.jboss.weld.bootstrap.ConcurrentValidator$1.doWork(ConcurrentValidator.java:68)
    at org.jboss.weld.bootstrap.ConcurrentValidator$1.doWork(ConcurrentValidator.java:66)
    at org.jboss.weld.executor.IterativeWorkerTaskFactory$1.call(IterativeWorkerTaskFactory.java:60)
    at org.jboss.weld.executor.IterativeWorkerTaskFactory$1.call(IterativeWorkerTaskFactory.java:53)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)

ago 07, 2018 5:43:37 PM org.apache.catalina.core.StandardContext startInternal
GRAVE: One or more listeners failed to start. Full details will be found in the appropriate container log file
ago 07, 2018 5:43:37 PM org.apache.catalina.core.StandardContext startInternal
GRAVE: Context [/vraptor-produtos] startup failed due to previous errors
ago 07, 2018 5:43:37 PM org.apache.catalina.core.StandardContext listenerStop
GRAVE: Exception sending context destroyed event to listener instance of class [org.jboss.weld.environment.servlet.Listener]
java.lang.NullPointerException
    at org.jboss.weld.servlet.WeldInitialListener.contextDestroyed(WeldInitialListener.java:102)
    at org.jboss.weld.servlet.api.helpers.ForwardingServletListener.contextDestroyed(ForwardingServletListener.java:30)
    at org.jboss.weld.environment.servlet.Listener.contextDestroyed(Listener.java:85)
    at org.apache.catalina.core.StandardContext.listenerStop(StandardContext.java:4690)
    at org.apache.catalina.core.StandardContext.stopInternal(StandardContext.java:5331)
    at org.apache.catalina.util.LifecycleBase.stop(LifecycleBase.java:257)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:187)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1427)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1417)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at org.apache.tomcat.util.threads.InlineExecutorService.execute(InlineExecutorService.java:75)
    at java.util.concurrent.AbstractExecutorService.submit(Unknown Source)
    at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:943)
    at org.apache.catalina.core.StandardHost.startInternal(StandardHost.java:839)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1427)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1417)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at org.apache.tomcat.util.threads.InlineExecutorService.execute(InlineExecutorService.java:75)
    at java.util.concurrent.AbstractExecutorService.submit(Unknown Source)
    at org.apache.catalina.core.ContainerBase.startInternal(ContainerBase.java:943)
    at org.apache.catalina.core.StandardEngine.startInternal(StandardEngine.java:258)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.StandardService.startInternal(StandardService.java:422)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.core.StandardServer.startInternal(StandardServer.java:770)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:183)
    at org.apache.catalina.startup.Catalina.start(Catalina.java:682)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at org.apache.catalina.startup.Bootstrap.start(Bootstrap.java:350)
    at org.apache.catalina.startup.Bootstrap.main(Bootstrap.java:492)

Já descobri qual era o problema. Eu tinha importado o Plugin da JPA que já tem o construtor de EntityManager. Com isso eu tinha que injetar o EntityManager direto nos Daos, sem criar o producer .