Have a fix in place, just adding some tests so this sort of thing doesn't happen again. I should be releasing 2.35.1 tonight.

In my case, "Override Global Settings" is not checked and "SMTP Server" is set but I get the error anyway.

Right, I was just commenting that if you want to override global settings, you have to fill in the values. It was not a comment about if this issue will show up or not.

Code changed in jenkins
User: Alex Earl
Path:
src/main/java/hudson/plugins/emailext/ExtendedEmailPublisherDescriptor.java
src/test/java/hudson/plugins/emailext/ExtendedEmailPublisherDescriptorTest.java
http://jenkins-ci.org/commit/email-ext-plugin/8c798f426dd706a275d3a5ea96c930f3b8b200bc
Log:
Fix JENKINS-20030

Reverted to older configure method code and added a simple round trip test to make sure exceptions don't occur.

Reverted to older form processing method and added test.

I am seeing the same thing; One installation each of Jenkins 1.534 and 1.509.4 with the version 2.35 plugin. Stack trace is below:

javax.servlet.ServletException: net.sf.json.JSONException: JSONObject["ext_mailer_smtp_server"] not found.
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:735)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:799)
at org.kohsuke.stapler.Stapler.invoke(Stapler.java:587)
at org.kohsuke.stapler.Stapler.service(Stapler.java:218)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:45)
at winstone.ServletConfiguration.execute(ServletConfiguration.java:248)
at winstone.RequestDispatcher.forward(RequestDispatcher.java:333)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:376)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:96)
at net.bull.javamelody.MonitoringFilter.doFilter(MonitoringFilter.java:208)
at net.bull.javamelody.MonitoringFilter.doFilter(MonitoringFilter.java:181)
at net.bull.javamelody.PluginMonitoringFilter.doFilter(PluginMonitoringFilter.java:86)
at org.jvnet.hudson.plugins.monitoring.HudsonMonitoringFilter.doFilter(HudsonMonitoringFilter.java:84)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:99)
at hudson.plugins.greenballs.GreenBallFilter.doFilter(GreenBallFilter.java:58)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:99)
at hudson.plugins.scm_sync_configuration.extensions.ScmSyncConfigurationFilter$1.call(ScmSyncConfigurationFilter.java:46)
at hudson.plugins.scm_sync_configuration.ScmSyncConfigurationDataProvider.provideRequestDuring(ScmSyncConfigurationDataProvider.java:103)
at hudson.plugins.scm_sync_configuration.extensions.ScmSyncConfigurationFilter.doFilter(ScmSyncConfigurationFilter.java:42)
at hudson.util.PluginServletFilter$1.doFilter(PluginServletFilter.java:99)
at hudson.util.PluginServletFilter.doFilter(PluginServletFilter.java:88)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:194)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:366)
at hudson.security.csrf.CrumbFilter.doFilter(CrumbFilter.java:48)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:194)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:366)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:84)
at hudson.security.UnwrapSecurityExceptionFilter.doFilter(UnwrapSecurityExceptionFilter.java:51)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ExceptionTranslationFilter.doFilter(ExceptionTranslationFilter.java:117)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.providers.anonymous.AnonymousProcessingFilter.doFilter(AnonymousProcessingFilter.java:125)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.rememberme.RememberMeProcessingFilter.doFilter(RememberMeProcessingFilter.java:142)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.AbstractProcessingFilter.doFilter(AbstractProcessingFilter.java:271)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.ui.basicauth.BasicProcessingFilter.doFilter(BasicProcessingFilter.java:174)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at jenkins.security.ApiTokenFilter.doFilter(ApiTokenFilter.java:64)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at org.acegisecurity.context.HttpSessionContextIntegrationFilter.doFilter(HttpSessionContextIntegrationFilter.java:249)
at hudson.security.HttpSessionContextIntegrationFilter2.doFilter(HttpSessionContextIntegrationFilter2.java:67)
at hudson.security.ChainedServletFilter$1.doFilter(ChainedServletFilter.java:87)
at hudson.security.ChainedServletFilter.doFilter(ChainedServletFilter.java:76)
at hudson.security.HudsonFilter.doFilter(HudsonFilter.java:164)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:194)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:366)
at org.kohsuke.stapler.compression.CompressionFilter.doFilter(CompressionFilter.java:46)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:194)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:366)
at hudson.util.CharacterEncodingFilter.doFilter(CharacterEncodingFilter.java:81)
at winstone.FilterConfiguration.execute(FilterConfiguration.java:194)
at winstone.RequestDispatcher.doFilter(RequestDispatcher.java:366)
at winstone.RequestDispatcher.forward(RequestDispatcher.java:331)
at winstone.RequestHandlerThread.processRequest(RequestHandlerThread.java:227)
at winstone.RequestHandlerThread.run(RequestHandlerThread.java:150)
at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:471)
at java.util.concurrent.FutureTask$Sync.innerRun(FutureTask.java:334)
at java.util.concurrent.FutureTask.run(FutureTask.java:166)
at winstone.BoundedExecutorService$1.run(BoundedExecutorService.java:77)
at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1145)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:615)
at java.lang.Thread.run(Thread.java:724)
Caused by: net.sf.json.JSONException: JSONObject["ext_mailer_smtp_server"] not found.
at net.sf.json.JSONObject.getString(JSONObject.java:2040)
at hudson.plugins.emailext.ExtendedEmailPublisherDescriptor.configure(ExtendedEmailPublisherDescriptor.java:314)
at jenkins.model.Jenkins.configureDescriptor(Jenkins.java:2791)
at jenkins.model.Jenkins.doConfigSubmit(Jenkins.java:2754)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:297)
at org.kohsuke.stapler.Function.bindAndInvoke(Function.java:160)
at org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:95)
at org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:111)
at org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:53)
at org.kohsuke.stapler.Stapler.tryInvoke(Stapler.java:685)
... 63 more

Having the same problem.
Running on Jenkins 1.535 & Email-ext plugin version 2.35.
Seeing the same Stack trace as Larry when trying to save system configuration.

Yes, 2.35.1 was released to fix this issue.

It is OK now with 2.35.1!

Fixed in 2.35.1