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